<PAGE>

                                                                     EXHIBIT 4.1
                                     WARRANT

THIS WARRANT AND THE SHARES ISSUABLE UPON EXERCISE HEREOF HAVE NOT BEEN
REGISTERED WITH THE SECURITIES AND EXCHANGE COMMISSION IN RELIANCE UPON AN
EXEMPTION FROM REGISTRATION UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND,
ACCORDINGLY, MAY NOT BE OFFERED OR SOLD EXCEPT PURSUANT TO AN EFFECTIVE
REGISTRATION STATEMENT OR PURSUANT TO AN AVAILABLE EXEMPTION FROM THE
REGISTRATION REQUIREMENTS OF THE SECURITIES ACT.

                           COSINE COMMUNICATIONS, INC.

                               WARRANT TO PURCHASE

                             SHARES OF COMMON STOCK

                              Expires May 28, 2006

                                                        Redwood City, California
                                               ORIGINAL ISSUE DATE: May 28, 2004

      FOR VALUE RECEIVED, subject to the provisions hereinafter set forth, the
undersigned, COSINE COMMUNICATIONS, INC., a Delaware corporation (together with
its successors and assigns, the "ISSUER"), hereby certifies that:

                  FUJITSU NETWORK COMMUNICATIONS, INC. ("FNC")

is entitled to subscribe for and purchase, during the period specified in this
Warrant, up to 254,489 shares (subject to adjustment as hereinafter provided) of
the duly authorized, validly issued, fully paid and non-assessable Common Stock,
$.0001 Par Value, of the Issuer, at an exercise price per share equal to the
Warrant Price then in effect, subject, however, to the provisions and upon the
terms and conditions hereinafter set forth. Initially capitalized terms used in
this Warrant and not otherwise defined herein shall have the respective meanings
specified in Section 7 hereof.

      1.    Term. The right to subscribe for and purchase shares of Warrant
Stock represented hereby shall commence on the Original Issue Date of this
Warrant as set forth above and shall expire at 5:00 p.m., Pacific Time, on the
second anniversary of the Original Issue Date (such period being the "TERM").

      2.    Method of Exercise Payment: Issuance of New Warrant: Transfer and
Exchange.

      (a)   Time of Exercise. The purchase rights represented by this Warrant
may be

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exercised only: (i) during the Term; (ii) as to all, but not less than all of
the Warrant Stock purchasable hereunder; and (iii) if, after the Original Issue
Date, any person or entity other than FNC or an affiliate of FNC shall have
acquired greater than 50 percent equity interest in the Issuer or shall own or
control more than 50 percent of the voting Securities of the Issuer.

      (b)   Method of Exercise. The Holder hereof may exercise this Warrant, as
to all, but not less than all, of the Warrant Stock, by the surrender of this
Warrant (with the Warrant Exercise Form attached hereto duly executed) at the
principal office of the Issuer (or at the office of the Warrant Agent designated
pursuant to Section 12), and by the payment to the Issuer of an amount of
consideration therefor equal to the Warrant Price in effect on the date of such
exercise multiplied by the number of shares of Warrant Stock with respect to
which this Warrant is then being exercised, payable by certified or official
bank check.

      (c)   Issuance of Stock Certificates. In the event of any exercise of the
rights represented by this Warrant in accordance with and subject to the terms
and conditions hereof, certificates for the shares of Warrant Stock so purchased
shall be dated the date of such exercise and delivered to the Holder hereof
within a reasonable time, not exceeding five Trading Days after such exercise,
and the Holder hereof shall be deemed for all purposes to be the Holder of the
shares of Warrant Stock so purchased as of the date of such exercise.

      (d)   Transferability of Warrant. Neither this Warrant, nor any interest
herein, may be transferred by FNC without the prior written consent of the
Issuer, which consent may be granted or withheld in the sole discretion of the
Issuer. If transferred pursuant to this paragraph, and subject to the provisions
of subsection (e) of this Section 2, this Warrant may be transferred on the
books of the Issuer by FNC hereof in person or by duly authorized attorney, upon
surrender of this Warrant at the principal office of the Issuer (or at the
office of the Warrant Agent designated pursuant to Section 12), properly
endorsed for transfer and upon payment of any necessary transfer tax or other
governmental charge imposed upon such transfer. Any Warrant issued on transfer
shall be dated the Original Issue Date and shall be identical with this Warrant.

      (e)   Compliance with Securities Laws.

            (i)   This Warrant is being issued pursuant to the terms of that
      certain Resale Agreement dated as of the Original Issue Date between FNC
      and the Issuer. The Resale Agreement is being entered into as an
      independent commercial transaction and not as an investment vehicle for
      FNC. FNC acknowledges that neither the Issuer nor any of the Issuer's
      officers, directors or employees, has made any representations or
      warranties as to the Issuer's financial condition, results or operations
      or business prospects or as to the advantages or disadvantages of holding
      or acquiring the Warrant or any Warrant Shares. FNC has made its own
      independent investigation as to such matters and has had an opportunity to
      inquire of the Issuer and of independent sources as to all such matters.

            (ii)  By accepting this Warrant, FNC acknowledges that this Warrant
      and the shares of Warrant Stock to be issued upon exercise hereof are
      being acquired solely for FNC's own account and not as a nominee for any
      other party or for resale or distribution thereof, and that FNC will not
      offer, sell or otherwise dispose of this Warrant or any

                                      -2-
<PAGE>

      shares of Warrant Stock to be issued upon exercise hereof except pursuant
      to an effective registration statement, or an exemption from registration,
      under the Securities Act and any applicable state securities laws.

            (iii) Except as provided in paragraph (iv) below, this Warrant and
      all certificates representing shares of Warrant Stock issued upon exercise
      hereof shall be stamped or imprinted with a legend in substantially the
      following form:

                  THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED
            WITH THE SECURITIES AND EXCHANGE COMMISSION IN RELIANCE UPON AN
            EXEMPTION FROM REGISTRATION UNDER THE SECURITIES ACT OF 1933, AS
            AMENDED, AND, ACCORDINGLY, MAY NOT BE OFFERED OR SOLD EXCEPT
            PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT OR PURSUANT TO AN
            AVAILABLE EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF THE
            SECURITIES ACT.

            (iv)  The restrictions imposed by this subsection (e) upon the
      transfer of this Warrant and the shares of Warrant Stock to be purchased
      upon exercise hereof shall terminate: (A) when such securities shall have
      been effectively registered under the Securities Act, (B) upon the
      Issuer's receipt of an opinion of counsel, in form and substance
      reasonably satisfactory to the Issuer, addressed to the Issuer to the
      effect that such restrictions are no longer required to ensure compliance
      with the Securities Act or (C) upon the Issuer's receipt of other evidence
      reasonably satisfactory to the Issuer that such registration is not
      required. Whenever such restrictions shall cease and terminate as to any
      such securities, the Holder thereof shall be entitled to receive from the
      Issuer (or its Warrant Agent or its transfer agent and registrar), without
      expense (other than applicable transfer taxes, if any), a new Warrant (or,
      in the case of shares of Warrant Stock, new stock certificates) of like
      tenor not bearing the applicable legends required by paragraph (ii) above
      relating to the Securities Act and state securities laws. Notwithstanding
      any other provision of this Warrant to the contrary, however, removal of
      the restrictions imposed by this subsection (e) shall not affect the
      restriction contained in subsection 2.(d) and any new Warrant shall bear a
      legend prominently referring to such restriction.

      3.    Stock Fully Paid: Reservation of Shares: Covenants.

      (a)   Stock Fully Paid. The Issuer represents, warrants, covenants and
agrees that all shares of Warrant Stock which may be issued upon the exercise of
this Warrant or otherwise hereunder will, upon issuance, be duly authorized,
validly issued, fully paid and non-assessable and free from all taxes, liens and
charges created by or through Issuer. The Issuer further covenants and agrees
that during the period within which this Warrant may be exercised, the Issuer
will at all times have authorized and reserved for the purpose of the issue upon
exercise of this Warrant a sufficient number of shares of the Issuer's Common
Stock to provide for the exercise of this Warrant.

      (b)   Issuer Covenants. The Issuer shall not by any action including,
without limitation,

                                      -3-
<PAGE>

amending the Certificate of Incorporation or the by-laws of the Issuer, or
through any reorganization, transfer of assets, consolidation, merger,
dissolution, issue or sale of securities or any other action, avoid or seek to
avoid the observance or performance of any of the terms of this Warrant, but
will at all times in good faith assist in the carrying out of all such terms and
in the taking of all such actions as may be necessary or appropriate to protect
the rights of the Holder hereof against dilution (to the extent specifically
provided herein) or impairment. Without limiting the generality of the
foregoing, the Issuer: (i) will not permit the par value of its Common Stock to
exceed the then effective Warrant Price, and (ii) will take all such action as
may be reasonably necessary in order that the Issuer may validly and legally
issue fully paid and nonassessable shares of its Common Stock, free and clear of
any liens, claims, encumbrances and restrictions (other than as provided herein)
upon the exercise of this Warrant.

      (c)   Loss, Theft, Destruction of Warrant. Upon receipt of evidence
satisfactory to the Issuer of the ownership of and the loss, theft, destruction
or mutilation of the Warrant and, in the case of any such loss, theft or
destruction, upon receipt of indemnity or security satisfactory to the Issuer
or, in the case of any such mutilation, upon surrender and cancellation of such
Warrant, the Issuer will make and deliver, in lieu of such lost, stolen,
destroyed or mutilated Warrant, a new Warrant of like tenor and representing the
right to purchase the same number of shares of Common Stock.

      4.    Adjustment of Warrant Price and Warrant Share Number. The number and
kind of Securities purchasable upon the exercise of this Warrant and the Warrant
Price shall be subject to adjustment from time to time upon the happening of
certain events as follows:

            (a) Recapitalization, Reorganization, Reclassification,
Consolidation, Merger or Sale. (i) In case the Issuer after the Original Issue
Date shall do any of the following (each, a "TRIGGERING EVENT") (a) consolidate
with or merge into any other Person and the Issuer shall not be the continuing
or surviving corporation of such consolidation or merger, or (b) permit any
other Person to consolidate with or merge into the Issuer and the Issuer shall
be the continuing or surviving Person but, in connection with such consolidation
or merger, any Capital Stock of the Issuer shall be changed into or exchanged
for Securities of any other Person or cash or any other property, or (c)
transfer all or substantially all of its properties or assets to any other
Person, or (d) effect a capital reorganization or reclassification of its
Capital Stock, then, and in the case of each such Triggering Event, proper
provision shall be made so that, upon the basis and the terms and in the manner
provided in this Warrant, the Holder of this Warrant shall be entitled (x) upon
the exercise hereof at any time after the consummation of such Triggering Event,
to the extent this Warrant is not exercised prior to such Triggering Event, or
is redeemed in connection with such Triggering Event, to receive at the Warrant
Price in effect at the time immediately prior to the consummation of such
Triggering Event in lieu of the Common Stock issuable upon such exercise of this
Warrant prior to such Triggering Event, the Securities, cash and property to
which such Holder would have been entitled upon the consummation of such
Triggering Event if such Holder had exercised the rights represented by this
Warrant immediately prior thereto, subject to adjustments and increases
(subsequent to such corporate action) as nearly equivalent as possible to the
adjustments provided for in Section 4 hereof or (y) to sell this Warrant to the
Person continuing after or surviving such Triggering Event, or to the Issuer (if
Issuer is the continuing or surviving Person) at a sales price equal to the
amount of cash, property and/or

                                      -4-
<PAGE>

Securities to which a holder of the number of shares of Common Stock which would
otherwise have been delivered upon the exercise of this Warrant would have been
entitled upon the effective date or closing of any such Triggering Event (the
"EVENT CONSIDERATION"), less the amount or portion of such Event Consideration
having a fair value equal to the aggregate Warrant Price applicable to this
Warrant.

      (ii)  Notwithstanding anything contained in this Warrant to the contrary,
the Issuer will not effect any Triggering Event unless, prior to the
consummation thereof, each Person (other than the Issuer) which may be required
to deliver any Securities, cash or property upon the exercise of this Warrant as
provided herein shall assume, by written instrument delivered to, and reasonably
satisfactory to, the Holder of this Warrant, (A) the obligations of the Issuer
under this Warrant (and if the Issuer shall survive the consummation of such
Triggering Event, such assumption shall be in addition to, and shall not release
the Issuer from, any continuing obligations of the Issuer under this Warrant)
and (B) the obligation to deliver to such Holder such shares of Securities, cash
or property as, in accordance with the foregoing provisions of this subsection
(a), such Holder shall be entitled to receive, and such Person shall have
similarly delivered to such Holder an opinion of counsel for such Person, which
counsel shall be reasonably satisfactory to such Holder, stating that this
Warrant shall thereafter continue in full force and effect and the terms hereof
[including, without limitation, all of the provisions of this subsection (a)]
shall be applicable to the Securities, cash or property which such Person may be
required to deliver upon any exercise of this Warrant or the exercise of any
rights pursuant hereto.

      (iii) If with respect to any Triggering Event, the Holder of this Warrant
has exercised its right as provided in clause (y) of subparagraph (i) of this
subsection (a) to sell this Warrant, the Issuer agrees that as a condition to
the consummation of any such Triggering Event the Issuer shall secure such right
of Holder to sell this Warrant to the Person continuing after or surviving such
Triggering Event and the Issuer shall not effect any such Triggering Event
unless upon or prior to the consummation thereof the amounts of cash, property
and/or Securities required under such clause (y) are delivered to the Holder of
this Warrant. The obligation of the Issuer to secure such right of the Holder to
sell this Warrant shall be subject to such Holder's cooperation with the Issuer,
including, without limitation, the giving of representations and warranties
comparable to the those given to the purchaser in the Securities purchase or
other agreement in connection with any such sale. Prior notice of any Triggering
Event shall be given to the Holder of this Warrant in accordance with Section 11
hereof.

      (b)   Subdivision or Combination of Shares. If the Issuer, at any time
while this Warrant is outstanding, shall subdivide or combine any shares of its
Common Stock, (i) in case of subdivision of shares, the Warrant Price shall be
proportionately reduced (as at the effective date of such subdivision or, if the
Issuer shall take a record of Holders of its Common Stock for the purpose of so
subdividing, as at the applicable record date, whichever is earlier) to reflect
the increase in the total number of shares of Common Stock outstanding as a
result of such subdivision, or (ii) in the case of a combination of shares, the
Warrant Price shall be proportionately increased (as at the effective date of
such combination or, if the Issuer shall take a record of Holders of its Common
Stock for the purpose of so combining, as at the applicable record date,
whichever is earlier) to reflect the reduction in the total number of shares of

                                      -5-
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Common Stock outstanding as a result of such combination.

      (c)   Certain Dividends and Distributions. If the Issuer, at any time
while this Warrant is outstanding, shall:

            (i)   Stock Dividends. Pay a dividend in, or make any other
      distribution to its stockholders (without consideration therefore) of,
      shares of Common Stock, the Warrant Price shall be adjusted, as at the
      date the Issuer shall take a record of the Holders of the Issuer's Capital
      Stock for the purpose of receiving such dividend or other distribution (or
      if no such record is taken, as at the date of such payment or other
      distribution), to that price determined by multiplying the Warrant Price
      in effect immediately prior to such record date (or if no such record is
      taken, then immediately prior to such payment or other distribution), by a
      fraction (1) the numerator of which shall be the total number of shares of
      Common Stock outstanding immediately prior to such dividend or
      distribution, and (2) the denominator of which shall be the total number
      of shares of Common Stock outstanding immediately after such dividend or
      distribution (plus in the event that the Issuer paid cash for fractional
      shares, the number of additional shares which would have been outstanding
      had the Issuer issued fractional shares in connection with said
      dividends); or

            (ii)  Other Dividends. At any time within the Term when this Warrant
      shall be exercisable under the provisions of clause 2.(a)(iii), pay a
      dividend on, or make any distribution of its assets upon or with respect
      to (including, but not limited to, a distribution of its property as a
      dividend in liquidation or partial liquidation or by way of a return of
      capital), the Common stock [other than as described in clause (i) of this
      subsection (c)], or in the event that the Issuer shall offer options or
      rights to subscribe for shares of Common Stock, or issue any Common Stock
      Equivalents, to all of its holders of Common Stock, then on the record
      date for such payment, distribution or offer, and upon exercise of the
      Warrant, the Holder shall receive what the Holder would have received had
      it exercised this Warrant in full immediately prior to the record date of
      such payment, distribution or offer or, in the absence of a record date,
      immediately prior to the date of such payment, distribution or offer.

      (d)   Issuance of Additional Shares of Common Stock. If the Issuer, at any
time while this Warrant is outstanding, shall issue any Additional Shares of
Common Stock (otherwise than as provided in the foregoing subsections (a)
through (c) of this Section 4), at a price per share less than the Warrant Price
then in effect or less than the Per Share Market Value then in effect or without
consideration, then the Warrant Price upon each such issuance shall be adjusted
to that price (rounded to the nearest cent) determined by multiplying the
Warrant Price then in effect by a fraction:

            (i)   the numerator of which shall be equal to the sum of (A) the
      number of shares of Common Stock outstanding immediately prior to the
      issuance of such Additional Shares of Common Stock PLUS (B) the number of
      shares of Common Stock (rounded to the nearest whole share) which the
      aggregate consideration for the total number of such Additional Shares of
      Common Stock so issued would purchase at a price

                                      -6-
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      per share equal to the greater of the Per Share Market Value then in
      effect and the Warrant Price then in effect, and

            (ii)  the denominator of which shall be equal to the number of
      shares of Common Stock outstanding immediately after the issuance of such
      Additional Shares of Common Stock.

The provisions of this subsection (d) shall not apply under any of the
circumstances for which an adjustment is provided in subsections (a), (b) or (c)
of this Section 4. No adjustment of the Warrant Price shall be made under this
subsection (d) upon the issuance of any Additional Shares of Common Stock which
are issued pursuant to any Common Stock Equivalent if upon the issuance of such
Common Stock Equivalent (x) any adjustment shall have been made pursuant to
subsection (e) of this Section 4 or (Y) no adjustment was required pursuant to
subsection (e) of this Section 4. No adjustment of the Warrant Price shall be
made under this subsection (d) in an amount less than $.01 per share, but any
such lesser adjustment shall be carried forward and shall be made at the time
and together with the next subsequent adjustment, if any, which together with
any adjustments so carried forward shall amount to $.01 per share or more,
provided that upon any adjustment of the Warrant Price as a result of any
dividend or distribution payable in Common Stock or Convertible Securities or
the reclassification, subdivision or combination of Common Stock into a greater
or smaller number of shares, the foregoing figure of $.01 per share (or such
figure as last adjusted) shall be adjusted (to the nearest one-half cent) in
proportion to the adjustment in the Warrant Price.

      (e)   Issuance of Common Stock Equivalents. If the Issuer, at any time
while this Warrant is outstanding, shall issue any Common Stock Equivalent and
the price per share for which Additional Shares of Common Stock may be issuable
thereafter pursuant to such Common Stock Equivalent shall be less than the
Warrant Price then in effect or less than the Per Share Market Value then in
effect, or if, after any such issuance of Common Stock Equivalents, the price
per share for which Additional Shares of Common Stock may be issuable thereafter
is amended or adjusted, and such price as so amended shall be less than the
Warrant Price or less than the Per Share Market Value in effect at the time of
such amendment, then the Warrant Price upon each such issuance or amendment
shall be adjusted as provided in the first sentence of subsection (d) of this
Section 4 on the basis that (1) the maximum number of Additional Shares of
Common Stock issuable pursuant to all such Common Stock Equivalents shall be
deemed to have been issued (whether or not such Common Stock Equivalents are
actually then exercisable, convertible or exchangeable in whole or in part) as
of the earlier of (A) the date on which the Issuer shall enter into a firm
contract for the issuance of such Common Stock Equivalent, or (B) the date of
actual issuance of such Common Stock Equivalent, and (2) the aggregate
consideration for such maximum number of Additional Shares of Common Stock shall
be deemed to be the minimum consideration received or receivable by the Issuer
for the issuance of such Additional Shares of Common Stock pursuant to such
Common Stock Equivalent. No adjustment of the Warrant Price shall be made under
this subsection (e) upon the issuance of any Convertible Security which is
issued pursuant to the exercise of any warrants or other subscription or
purchase rights therefore, if any adjustment shall previously have been made in
the Warrant Price then in effect upon the issuance of such warrants or other
rights pursuant to this subsection (e). If no adjustment is required under this
subsection (e) upon issuance of any

                                      -7-
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Common Stock Equivalent or once an adjustment is made under this subsection (e)
based upon the Per Share Market Value in effect on the date of such adjustment,
no further adjustment shall be made under this subsection (e) based solely upon
a change in the Per Share Market Value after such date.

      (f)   Purchase of Common Stock by the Issuer. If the Issuer at any time
while this Warrant is outstanding shall, directly or indirectly through a
Subsidiary or otherwise, purchase, redeem or otherwise acquire any shares of
Common Stock at a price per share greater than the Per Share Market Value then
in effect, then the Warrant Price upon each such purchase, redemption or
acquisition shall be adjusted to that price determined by multiplying such
Warrant Price by a fraction (i) the numerator of which shall be the number of
shares of Common Stock outstanding immediately prior to such purchase,
redemption or acquisition minus the number of shares of Common Stock which the
aggregate consideration for the total number of such shares of Common Stock so
purchased, redeemed or acquired would purchase at the Per Share Market Value;
and (ii) the denominator of which shall be the number of shares of Common Stock
outstanding immediately after such purchase, redemption or acquisition. For the
purposes of this subsection (f), the date as of which the Per Share Market Value
shall be computed shall be the earlier of (x) the date on which the Issuer shall
enter into a firm contract for the purchase, redemption or acquisition of such
Common Stock, or (y) the date of actual purchase, redemption or acquisition of
such Common Stock. For the purposes of this subsection (f), a purchase,
redemption or acquisition of a Common Stock Equivalent shall be deemed to be a
purchase of the underlying Common Stock, and the computation herein required
shall be made on the basis of the full exercise, conversion or exchange of such
Common Stock Equivalent on the date as of which such computation is required
hereby to be made, whether or not such Common Stock Equivalent is actually
exercisable, convertible or exchangeable on such date.

      (g)   Other Provisions Applicable to Adjustments Under this Section 4. The
following provisions shall be applicable to the making of adjustments in the
Warrant Price hereinbefore provided in Section 4:

            (i)   Computation of Consideration. The consideration received by
      the Issuer shall be deemed to be the following: to the extent that any
      Additional Shares of Common Stock or any Common Stock Equivalents shall be
      issued for a cash consideration, the consideration received by the Issuer
      therefore, or if such Additional Shares of Common Stock or Common Stock
      Equivalents are offered by the Issuer for subscription, the subscription
      price, or, if such Additional Shares of Common Stock or Common Stock
      Equivalents are sold to underwriters or dealers for public offering
      without a subscription offering, the public offering price, in any such
      case excluding any amounts paid or receivable for accrued interest or
      accrued dividends and without deduction of any compensation, discounts,
      commissions, or expenses paid or incurred by the Issuer for or in
      connection with the underwriting thereof or otherwise in connection with
      the issue thereof; to the extent that such issuance shall be for a
      consideration other than cash, then, except as herein otherwise expressly
      provided, the fair market value of such consideration at the, time of such
      issuance as determined in good faith by the Board. The consideration for
      any Additional Shares of Common Stock issuable pursuant to any Common
      Stock Equivalents shall be the consideration received by the Issuer for
      issuing such Common

                                      -8-
<PAGE>

      Stock Equivalents, plus the additional consideration payable to the Issuer
      upon the exercise, conversion or exchange of such Common Stock
      Equivalents. In case of the issuance at any time of any Additional Shares
      of Common Stock or Common Stock Equivalents in payment or satisfaction of
      any dividend upon any class of Capital Stock of the Issuer other than
      Common Stock, the Issuer shall be deemed to have received for such
      Additional Shares of Common Stock or Common Stock Equivalents a
      consideration equal to the amount of such dividend so paid or satisfied.
      In any case in which the consideration to be received or paid shall be
      other than cash, the Board shall notify the Holder of this Warrant of its
      determination of the fair market value of such consideration prior to
      payment or accepting receipt thereof. If, within thirty days after receipt
      of said notice, the Majority Holders shall notify the Board in writing of
      their objection to such determination, a determination of the fair market
      value of such consideration shall be made by an Independent Appraiser
      selected by the Majority Holders with the approval of the Board (which
      approval shall not be unreasonably withheld), whose fees and expenses
      shall be paid by the Issuer.

            (ii)  Readjustment of Warrant Price. Upon the expiration or
      termination of the right to convert, exchange or exercise any Common Stock
      Equivalent the issuance of which effected an adjustment in the Warrant
      Price, if such Common Stock Equivalent shall not have been converted,
      exercised or exchanged in its entirety, the number of shares of Common
      Stock deemed to be issued and outstanding by reason of the fact that they
      were issuable upon conversion, exchange or exercise of any such Common
      Stock Equivalent shall no longer be computed as set forth above, and the
      Warrant Price shall forthwith be readjusted and thereafter be the price
      which it would have been (but reflecting any other adjustments in the
      Warrant Price made pursuant to the provisions of this Section 4 after the
      issuance of such Common Stock Equivalent) had the adjustment of the
      Warrant Price been made in accordance with the issuance or sale of the
      number of Additional Shares of Common Stock actually issued upon
      conversion, exchange or issuance of such Common Stock Equivalent and
      thereupon only the number of Additional Shares of Common Stock actually so
      issued shall be deemed to have been issued and only the consideration
      actually received by the Issuer [computed as in clause (i) of this
      subsection (g)] shall be deemed to have been received by the Issuer.

            (iii) Outstanding Common Stock. The number of shares of Common Stock
      at any time outstanding shall: (A) not include any shares thereof then
      directly or indirectly owned or held by or for the account of the Issuer
      or any of its Subsidiaries, and (B) be deemed to include all shares of
      Common Stock then issuable upon conversion, exercise or exchange of any
      then outstanding Common Stock Equivalents or any other evidences of
      Indebtedness, shares of Capital Stock (including, without limitation, any
      Preferred Stock) or other Securities which are or may be at any time
      convertible into or exchangeable for shares of Common Stock or Other
      Common Stock.

      (h)   Other Action Affecting Common Stock. In case after the Original
Issue Date the Issuer shall take any action affecting its Common Stock, other
than an action described in any of the foregoing subsections (a) through (g) of
this Section 4, inclusive, and the failure to make any adjustment would not
fairly protect the purchase rights represented by this Warrant in accordance

                                      -9-
<PAGE>

with the essential intent and principle of this Section 4, then the Warrant
Price shall be adjusted in such manner and at such time as the Board may in good
faith determine to be equitable in the circumstances.

      (i)   Adjustment of Warrant Share Number. Upon each adjustment in the
Warrant Price pursuant to any of the foregoing provisions of this Section 4, the
Warrant Share Number shall be adjusted, to the nearest one hundredth of a whole
share, to the product obtained by multiplying the Warrant Share Number
immediately prior to such adjustment in the Warrant Price by a fraction, the
numerator of which shall be the Warrant Price immediately before giving effect
to such adjustment and the denominator of which shall be the Warrant Price
immediately after giving effect to such adjustment. If the Issuer shall be in
default under any provision contained in Section 3 of this Warrant so that
shares issued at the Warrant Price adjusted in accordance with this Section 4
would not be validly issued, the adjustment of the Warrant Share Number provided
for in the foregoing sentence shall nonetheless be made and the Holder of this
Warrant shall be entitled to purchase such greater number of shares at the
lowest price at which such shares may then be validly issued under applicable
law. Such exercise shall not constitute a waiver of any claim arising against
the Issuer by reason of its default under Section 3 of this Warrant.

      (j)   Form of Warrant after Adjustments. The form of this Warrant need not
be changed because of any adjustments in the Warrant Price or the number and
kind of Securities purchasable upon the exercise of this Warrant.

      5.    Notice of Adjustments. Whenever the Warrant Price or Warrant Share
Number shall be adjusted pursuant to Section 4 hereof (for purposes of this
Section 5, each an "ADJUSTMENT"), the Issuer shall cause its Chief Financial
Officer to prepare and execute a certificate setting forth, in reasonable
detail, the event requiring the adjustment, the amount of the adjustment, the
method by which such adjustment was calculated (including a description of the
basis on which the Board made any determination hereunder, provided that such
notice shall not contain any material or non-public information), and the
Warrant Price and Warrant Share Number after giving effect to such adjustment,
and shall cause copies of such certificate to be delivered to the Holder of this
Warrant promptly after each adjustment. Any dispute between the Issuer and the
Holder of this Warrant with respect to the matters set forth in such certificate
may at the option of the Holder of this Warrant be submitted to an independent
public accounting firm of national stature, other than the firm which serves as
the independent auditor of the Issuer or the Holder, selected by the Holder,
provided that the Issuer shall have ten days after receipt of notice from such
Holder of its selection of such firm to object thereto, in which case such
Holder shall select another such firm and the Issuer shall have no such right of
objection. The firm selected by the Holder of this Warrant as provided in the
preceding sentence shall be instructed to deliver a written opinion as to such
matters to the Issuer and such Holder within 30 days after submission to it of
such dispute. Such opinion shall be final and binding on the parties hereto. The
fees and expenses of such accounting firm shall be paid by the Issuer.

      6.    Fractional Shares. No fractional shares of Warrant Stock will be
issued in connection with and exercise hereof, but in lieu of such fractional
shares, the Issuer shall make a cash payment therefore equal in amount to the
product of the applicable fraction multiplied by

                                      -10-
<PAGE>

the Per Share Market Value then in effect.

      7.    Definitions. For the purposes of this Warrant, the following
initially capitalized terms have the following meanings:

            "ADDITIONAL SHARES OF COMMON STOCK" means all shares of Common Stock
      issued by the Issuer after the Original Issue Date, and all shares of
      Other Common, if any, issued by the Issuer after the Original Issue Date,
      except (i) Warrant Stock, (ii) any shares of Common Stock issuable upon
      conversion of an authorized class or series of Preferred Stock (iii) any
      shares of Common Stock issuable upon exercise of stock options pursuant to
      the Issuer's 1997 Stock Option Plan, 2000 Stock Option Plan, 2002 Stock
      Option Plan or 2000 Director Option Plan.

            "BOARD" shall mean the Board of Directors of the Issuer.

            "CAPITAL STOCK" means and includes (i) any and all shares,
      interests, participations or other equivalents of or interests in (however
      designated) corporate stock, including, without limitation, shares of
      preferred or preference stock, (ii) all partnership interests (whether
      general or limited) in any Person which is a partnership, (iii) all
      membership interests or limited liability company interests in any limited
      liability company, and (iv) all equity or ownership interests in any
      Person of any other type.

            "CERTIFICATE OF INCORPORATION" means the Certificate of
      Incorporation of the Issuer as in effect on the Original Issue Date and as
      hereafter from time to time amended, modified, supplemented or restated in
      accordance with the terms hereof and thereof and pursuant to applicable
      law.

            "COMMON STOCK" means the Common Stock, $.0001 Par Value, of the
      Issuer and any other Capital Stock into which such stock may hereafter be
      changed.

            "COMMON STOCK EQUIVALENT" means any Convertible Security or warrant,
      option or other right to subscribe for or purchase any Additional Shares
      of Common Stock or any Convertible Security.

            "CONVERTIBLE SECURITIES" means evidences of Indebtedness, shares of
      Capital Stock or other Securities which are or may be at any time
      convertible into or exchangeable for Additional Shares of Common Stock.
      The term "CONVERTIBLE SECURITY" means one of the Convertible Securities.

            "GOVERNMENTAL AUTHORITY" means any governmental, regulatory or
      self-regulatory entity, department, body, official, authority, commission,
      board, agency or instrumentality, whether federal, state or local, and
      whether domestic or foreign.

            "HOLDERS" mean the Persons who shall from time to time own this
      Warrant. Use of the term "Holder" herein is for convenience and shall not
      limit the restrictions on transfer of this Warrant contained in Sections
      2.(d) and 2.(e).

                                      -11-
<PAGE>

            "INDEPENDENT APPRAISER" means a nationally recognized or major
      regional investment banking firm or firm of independent certified public
      accountants of recognized national standing (which may be the firm that
      regularly examines the financial statements of the Issuer) that is
      regularly engaged in the business of appraising the Capital Stock or
      assets of corporations or other entities as going concerns, and which is
      not affiliated with either the Issuer or the Holder of this Warrant.

            "ISSUER" means CoSine Communications, Inc., a Delaware corporation,
      and its successors.

            "NASDAQ" means the NASDAQ Stock Market, operated by the National
      Association of Securities Dealers, Inc.

            "OTHER COMMON STOCK" means any other Capital Stock of the Issuer of
      any class which shall be authorized at any time after the date of this
      Warrant (other than Common Stock) and which shall have the right to
      participate in the distribution of earnings and assets of the Issuer
      without limitation as to amount.

            "PERSON" means an individual, corporation, limited liability
      company, partnership, joint stock company, trust, unincorporated
      organization, joint venture, Governmental Authority or other entity of
      whatever nature.

            "PER SHARE MARKET VALUE" means on any particular date (a) the
      closing bid price per share of the Common Stock on such date on The Nasdaq
      SmallCap Market, the Nasdaq National Market or other registered national
      securities exchange on which the Common Stock is then listed or if there
      is no such price on such date, then the closing bid price on such exchange
      or quotation system on the date nearest preceding such date, or (b) if the
      Common Stock is not listed then on The Nasdaq SmallCap Market, the Nasdaq
      National Market or any registered national securities exchange, the
      closing bid price for a share of Common Stock in the over-the-counter
      market, as reported by the Nasdaq Stock Market or in the National
      Quotation Bureau Incorporated or similar organization or agency succeeding
      to its functions of reporting prices) at the close of business on such
      date, or (c) if the Common Stock is not then reported by the National
      Quotation Bureau Incorporated (or similar organization or agency
      succeeding to its functions of reporting prices), then the average of the
      "Pink Sheet" quotes for the relevant conversion period, as determined in
      good faith by the holder, or (d) if the Common Stock is not then publicly
      traded the fair market value of a share of Common Stock as determined by
      an Independent Appraiser selected in good faith by the Holder; provided,
      however, that the Issuer, after receipt of the determination by such
      Independent Appraiser, shall have the right to select an additional
      Independent Appraiser, in which case, the fair market value shall be equal
      to the average of the determinations by each such Independent Appraiser;
      and provided, further that all determinations of the Per Share Market
      Value shall be appropriately adjusted for any stock dividends, stock
      splits or other similar transactions during such period. The determination
      of fair market value by an Independent Appraiser shall be based upon the
      fair market value of the Issuer determined on a going concern

                                      -12-
<PAGE>

      basis as between a willing buyer and a willing seller and taking into
      account all relevant factors determinative of value, and shall be final
      and binding on all parties. In determining the fair market value of any
      shares of Common Stock, no consideration shall be given to any
      restrictions on transfer of the Common Stock imposed by agreement or by
      federal or state securities laws, or to the existence or absence of, or
      any limitations on, voting rights.

            "PREFERRED STOCK" means the Issuer's Preferred Stock, no shares of
      which were issued or outstanding on the Original Issue Date.

            "SECURITIES" means any debt or equity securities of the Issuer,
      whether now or hereafter authorized, any instrument convertible into or
      exchangeable for Securities or a Security, and any option, warrant or
      other right to purchase or acquire any Security. "Security" means one of
      the Securities.

            "SECURITIES ACT" means the Securities Act of 1933, as amended, or
      any similar federal statute then in effect.

            "SUBSIDIARY" means any corporation at least 50 percent of whose
      outstanding Voting Stock shall at the time be owned directly or indirectly
      by the Issuer or by one or more of its Subsidiaries, or by the Issuer and
      one or more of its Subsidiaries.

            "TRADING DAY" means (a) a day on which the Common Stock is listed on
      The Nasdaq SmallCap Market, the Nasdaq National Market or other registered
      national securities exchange on which the Common Stock has been listed, or
      (b) if the Common Stock is not listed on The Nasdaq SmallCap Market, the
      Nasdaq National Market or any registered national securities exchange, a
      day or which the Common Stock is quoted in the over-the-counter market, as
      reported by the OTC Bulletin Board, or (c) if the Common Stock is not
      quoted on the OTC Bulletin Board, a day on which the Common Stock is
      quoted in the over-the-counter market as reported by the National
      Quotation Bureau Incorporated (or any similar organization or agency
      succeeding its functions of reporting prices); provided, however, that in
      the event that the Common Stock is not listed or quoted as set forth in
      (a), (b) and (c) hereof, then Trading Day shall mean any day except
      Saturday, Sunday and any day which shall be a legal holiday or a day on
      which banking institutions in the State of California are authorized or
      required by law or other government action to close.

            "TERM" has the meaning specified in Section 1 hereof.

            "VOTING STOCK", as applied to the Capital Stock of any corporation,
      means Capital Stock of any class or classes (however designated) having
      ordinary voting power for the election of a majority of the members of the
      Board of Directors (or other governing body) of such corporation, other
      than Capital Stock having such power only by reason of the happening of a
      contingency.

            "WARRANT" means this Warrant issued to FNC pursuant to Section 10.4
      of that

                                      -13-
<PAGE>

      certain Resale Agreement between the Issuer and FNC dated the Original
      Issue Date.

            "WARRANT PRICE" means initially $4.65, as such price may be adjusted
      from time to time as shall result from the adjustments specified in
      Section 4 hereof.

            "WARRANT SHARE NUMBER" means at any time the aggregate number of
      shares of Warrant Stock which may at such time be purchased upon exercise
      of this Warrant, after giving effect to all prior adjustments and
      increases to such number made or required to be made under the terms
      hereof.

            "WARRANT STOCK" means Common Stock issuable upon exercise of any
      Warrant or Warrants or otherwise issuable pursuant to any Warrant or
      Warrants.

      8.    Other Notices. In case at any time:

                  (A)   the Issuer shall make any distributions to the holders
                        of Common Stock; or

                  (B)   the Issuer shall authorize the granting to all holders
                        of its Common Stock of rights to subscribe for or
                        purchase any shares of Capital Stock of any class or of
                        any Common Stock Equivalents or Convertible Securities
                        or other rights; or

                  (C)   there shall be any reclassification of the Capital Stock
                        of the Issuer; or

                  (D)   there shall be any capital reorganization by the Issuer;
                        or

                  (E)   there shall be any (i) consolidation or merger involving
                        the Issuer or (ii) sale, transfer or other disposition
                        of all or substantially all of the Issuer's property,
                        assets or business (except a merger or other
                        reorganization in which the Issuer shall be the
                        surviving corporation and its shares of Capital Stock
                        shall continue to be outstanding and unchanged and
                        except a consolidation, merger, sale, transfer or other
                        disposition involving a wholly-owned Subsidiary); or

                  (F)   there shall be a voluntary or involuntary dissolution,
                        liquidation or winding-up of the Issuer or any partial
                        liquidation of the Issuer or distribution to holders of
                        Common Stock;

then, in each of such cases, the Issuer shall give written notice to the Holder
of the date on which (i) the books of the Issuer shall close or a record shall
be taken for such dividend, distribution or subscription rights or (ii) such
reorganization, reclassification, consolidation, merger, disposition,

                                      -14-
<PAGE>

dissolution, liquidation or winding-up, as the case may be, shall take place.
Such notice also shall specify the date as of which the holders of Common Stock
of record shall participate in such dividend, distribution or subscription
rights, or shall be entitled to exchange their certificates for Common Stock for
securities or other property deliverable upon such reorganization,
reclassification, consolidation, merger, disposition, dissolution, liquidation
or winding-up, as the case may be. Such notice shall be given at least 20 days
prior to the action in question and not less than 20 days prior to the record
date or the date on which the Issuer's transfer books are closed in respect
thereto, but not prior to the public disclosure thereof. The Issuer shall give
to the Holder notice of all meetings and actions by written consent of its
stockholders, at the same time in the same manner as notice of any meetings of
stockholders is required to be given to stockholders who do not waive such
notice (or, if such requires no notice, then two Trading Days written notice
thereof describing the matters upon which action is to be taken). The Holder
shall have the right to send two representatives selected by it to each meeting,
who shall be permitted to attend, but not vote at, such meeting and any
adjournments thereof. This Warrant entitles the Holder to receive copies of all
financial and other information distributed or required to be distributed to the
holders of the Common Stock.

      9.    Amendment and Waiver. Any term, covenant, agreement or condition in
this Warrant may be amended, or compliance therewith may be waived (either
generally or in a particular instance and either retroactively or
prospectively), by a written instrument or written instruments executed by the
Issuer and the Holder.

      10.   Governing Law and Venue. This Warrant is made under the laws of the
state of California, excluding application of its conflicts of laws principles
and of the 1980 United Nations Convention on Contracts for the International
Sale of Goods. Any action to enforce the terms of this Warrant must be brought
in a court having jurisdiction in San Mateo County, California. In any legal
action or other proceeding brought to enforce a party's rights under this
Warrant, the prevailing party may recover attorneys' fees and other expenses
reasonably incurred in that action or proceeding, in addition to any other
relief to which the party is entitled.

                                      -15-
<PAGE>

      11.   Notices. Any notice, approval, consent, or other communication
required under this Warrant must be in writing and will be deemed given as
follows: (a) on the day delivered, if personally delivered, (b) on the 5th
business day after deposit in the mail if mailed, postage prepaid by certified
U.S. mail, return receipt requested, or (c) on the day sent, if transmitted by
facsimile transmission with confirmation, in each case addressed to the other
party at the address below.

      With respect to FNC:

            Fujitsu Network Communications, Inc.
            2801 Telecom Parkway
            Richardson, Texas 75082
            Telephone: (   )
            Facsimile: (   )

      With respect to the Issuer:

            CoSine Communications, Inc.
            1200 Bridge Parkway
            Redwood City, CA 94065
            Telephone: (650)
            Facsimile: (650) 637-2427

      Either party may designate a different place or places for notices by
delivering notice to the other party in accordance with this Section.

      12.   Warrant Agent. The Issuer may, by written notice to the Holder of
this Warrant, appoint an agent having an office in the State of California for
the purpose of issuing shares of Warrant Stock on the exercise of this Warrant
pursuant to subsection (b) of Section 2 hereof, exchanging this Warrant pursuant
to subsection (d) of Section 2 hereof or replacing this Warrant pursuant to
subsection (d) of Section 3 hereof, or any of the foregoing, and thereafter any
such issuance, exchange or replacement, as the case may be, shall be made at
such office by such agent.

      13.   Remedies. The Issuer stipulates that the remedies at law of the
Holder of this Warrant in the event of any default or threatened default by the
Issuer in the performance of or compliance with any of the terms of this Warrant
are not and will not be adequate and that, to the fullest extent permitted by
law, such terms may be specifically enforced by a decree for the specific
performance of any agreement contained herein or by an injunction against a
violation of any of the terms hereof or otherwise.

      14.   Successors and Assigns. This Warrant and the rights evidenced hereby
shall, subject to the restrictions on transfer contained in this Warrant, inure
to the benefit of and be binding upon the successors and assigns of the Issuer,
the Holder hereof and (to the extent provided herein) the Holder of Warrant
Stock issued pursuant hereto, and shall be enforceable by any such Holder or
Holder of Warrant Stock

                                      -16-
<PAGE>

      15.   Modification and Severability. If, in any action before any court or
agency legally empowered to enforce any provision contained herein, any
provision hereof is found to be unenforceable, then such provision shall be
deemed modified to the extent necessary to make it enforceable by such court or
agency. If any such provision is not enforceable as set forth in the preceding
sentence, the unenforceability of such provision shall not affect the other
provisions of this Warrant, but this Warrant shall be construed as if such
unenforceable provision had never been contained herein.

      16.   Headings. The headings of the Sections of this Warrant are for
convenience of reference only and shall not, for any purpose, be deemed a part
of this Warrant.

      IN WITNESS WHEREOF, the Parties have executed this Warrant as of the
Original Issue Date.

                                 COSINE COMMUNICATIONS, INC.

                                 By: [ILLEGIBLE]
                                     ---------------------------
                                     President

Warrant Accepted and Agreed as of the Original Issue Date:

FUJITSU NETWORK COMMUNICATIONS, INC.

By: [ILLEGIBLE]
   ------------------------------
ITS: Group President & Chief Operating Officer

032077\00002\569642 V006

                           COSINE COMMUNICATIONS, INC.

                              WARRANT EXERCISE FORM

              (Exercisable as to all, but not less than all shares)

The undersigned _______________, pursuant to the provisions of the within
Warrant, hereby elects to purchase _____ shares of Common Stock of CoSine
Communications, Inc. covered by the within Warrant.

                                      -17-
<PAGE>

Dated: _________________           Signature   _________________________________

                                   Address     _________________________________
                                               _________________________________
032077\00002\569642 V006

                                      -18-