<PAGE>   1
                             NETWORK SOLUTIONS, INC.
                            1996 STOCK INCENTIVE PLAN

                       NONSTATUTORY STOCK OPTION AGREEMENT


            Network Solutions, Inc., a Delaware corporation (the "Company"),
hereby grants an Option to purchase shares of its Class A Common Stock ("Common
Shares") to the Optionee named below. The terms and conditions of the Option are
set forth in this cover sheet, in the attached Agreement and in the Company's
1996 Stock Incentive Plan (the "Plan"), as amended and restated effective July
7, 1997.


Date of Grant:       5/21/99
               ------------------------------------------------------------

Name of Optionee:    James Rutt
                 ----------------------------------------------------------

Optionee's Social Security Number: ###-##-####
                                  -----------------------------------------

Number of Common Shares Covered by Option:     375,000
                                          ---------------------------------

Exercise Price per Common Share:    $64.00
                                -------------------------------------------

Vesting Start Date:     5/21/99
                   --------------------------------------------------------

Vesting Schedule: Subject to the attached Agreement, during your Service the
Option shall vest as to 30%, 30%, 20% and 20% of the Common Shares on the first
through fourth anniversaries, respectively, of the Vesting Start Date. In the
event your employment terminates due to death or disability, you will receive
pro rata vesting credit for each whole month of Service you complete. (For
example, the Option will be 15% vested if your employment terminates due to
disability 6 months after the Vesting Start Date.) Also, in the event your
employment is involuntarily terminated other than for Cause or Non-performance,
or you voluntarily terminate your employment for Good Reason, at the time of
termination you will be credited with an additional twelve (12) months of
Service for purposes of the Vesting Schedule. (For example, the Option will be
30% vested if your employment is terminated by the Company other than for Cause
or Non-performance or if you terminate your employment for Good Reason, before
the first anniversary of the Vesting Start Date. In addition to the additional
twelve (12) months of Service credited above, if applicable, in the event your
employment is involuntarily terminated other than for Cause or Non-performance,
or you voluntarily terminate your employment for Good Reason, in each case,
either immediately before or within eighteen months after a Change of Control
occurs, at the time of termination you will be credited with an additional
twelve (12) months of Service for purposes of the Vesting Schedule; provided,
however, that for this purpose, "Good Reason" shall not exist solely if, as a
result of the Change of Control, you become responsible for managing a company,
subsidiary or division which is engaged in substantially the same business as
the Company was engaged in immediately prior to the Change of Control. For
purposes of this Option, the term "Change in Control" shall mean (i) a Change in
Control as defined in the Plan, or (ii) approval by the stockholders of the


<PAGE>   2

Company of a reorganization, merger, consolidation, in each case, with respect
to which persons who were stockholders of the Company immediately prior to such
reorganization, merger or consolidation do not, immediately thereafter, own more
than 50% of the combined voting power entitled to vote generally in the election
of directors of the reorganized, merged or consolidated company's then
outstanding voting securities, or a liquidation or dissolution of the Company or
of the sale of all or substantially all of the assets of the Company.


            BY SIGNING THIS COVER SHEET, YOU VOLUNTARILY AGREE TO ALL OF THE
            TERMS AND CONDITIONS DESCRIBED IN THE ATTACHED AGREEMENT AND IN THE
            PLAN, A COPY OF WHICH IS ALSO ATTACHED.


Optionee:  /s/   JAMES P. RUTT
           ---------------------------------------------------------------------
                                    (Signature)

Company:  /s/    ROBERT J. KORZENIEWSKI
          ---------------------------------------------------------------------
                                    (Signature)

          Title:   CFO
                  -------------------------------------------------------------


                                       2
<PAGE>   3


                             NETWORK SOLUTIONS, INC.
                            1996 STOCK INCENTIVE PLAN

                       NONSTATUTORY STOCK OPTION AGREEMENT


NONSTATUTORY STOCK                         This Option is not intended to be an
OPTION                                     incentive stock option under section
                                           422 of the Internal Revenue Code and
                                           will be interpreted accordingly.

VESTING                                    Your right to exercise this Option
                                           vests during your Service as shown on
                                           the cover sheet. The number of vested
                                           Common Shares shall be rounded to the
                                           next lower whole number. No
                                           additional Common Shares will vest
                                           after your Service has terminated for
                                           any reason, except as provided
                                           herein.

                                           For purposes of this Option, the term
                                           "Cause" shall mean (i) your
                                           conviction of a felony involving a
                                           personal act of willful and
                                           intentional misconduct or the entry
                                           by you of a plea of nolo contendere
                                           in connection with such an alleged
                                           felony.

                                           For purposes of this Option, the term
                                           "Non-performance" shall mean (i) the
                                           repeated and continual failure by you
                                           to fulfill the basic duties of your
                                           positions(s) with the Company; (ii)
                                           your gross negligence, dishonesty,
                                           willful malfeasance or gross
                                           misconduct in connection with your
                                           employment with the Company which has
                                           had (or is expected to have) a
                                           demonstrative and adverse effect on
                                           the business or reputation of the
                                           Company or its subsidiaries; or (iii)
                                           failure by you to follow any lawful
                                           directive established for you by the
                                           Board of Directors. Notwithstanding,
                                           the foregoing, "Non-performance"
                                           shall not be deemed to exist unless
                                           you have been given an opportunity to
                                           be heard by the Board of Directors
                                           after at least 10 days' written
                                           notice by the Board. In addition, for
                                           purposes of the definition of
                                           "Non-performance," any isolated,
                                           insubstantial and inadvertent action
                                           not taken in bad faith which is
                                           remedied by you promptly after
                                           receipt of written notice thereof
                                           from the Company shall not be deemed
                                           to be "Non-performance."

                                           For purposes of this Option, the term
                                           "Good Reason" shall mean the
                                           occurrence of any of the following
                                           without your written consent: (i)
                                           assignment to you of any duties
                                           materially inconsistent with your
                                           position as Chief Executive Officer
                                           or any material diminution in your
                                           position, authority, duties or
                                           responsibilities; (ii) reduction in
                                           base salary or target bonus
                                           opportunity or failure to provide you
                                           with stock option grants on a basis
                                           which is at least as favorable as
                                           that provided to other executive
                                           officers generally (excluding grants
                                           to new hires or other extraordinary
                                           grants to a particular individual);
                                           (iii) relocation of your principal
                                           work place to a location that is more


                                       3
<PAGE>   4

                                           than 25 miles from Reston, Virginia;
                                           or (iv) failure to be elected or
                                           reelected to the NSI Board of
                                           Directors or removal from the NSI
                                           Board of Directors. For purposes of
                                           the definition of "Good Reason," any
                                           isolated, insubstantial and
                                           inadvertent action not taken in bad
                                           faith which is remedied by NSI
                                           promptly after receipt of written
                                           notice thereof from you shall not be
                                           deemed to be "Good Reason."

                                           This Option shall not be reduced as
                                           provided in, or be subject to,
                                           Article 14 of the Plan.

SERVICE                                    Your "Service" continues while you
                                           are actively employed by, or serving
                                           as a consultant to or director of,
                                           the Company or any Parent, Subsidiary
                                           or other affiliate of the Company
                                           determined in the sole discretion of
                                           the Company. For purposes of this
                                           Option, your Service does not
                                           terminate when you go on a bona fide
                                           leave of absence that was approved by
                                           the Company in writing, if the terms
                                           of the leave provide for continued
                                           Service crediting, or when continued
                                           Service crediting is required by
                                           applicable law. Your Service
                                           terminates in any event when the
                                           approved leave ends, unless you
                                           immediately return to active work.
                                           The Company determines which leaves
                                           shall be credited toward Service, and
                                           when your Service terminates, for all
                                           purposes under the Plan and
                                           this Agreement.

TERM                                       Your Option will expire in any event
                                           at the close of business at Company
                                           headquarters on the day before the
                                           fifth anniversary of the date of
                                           grant of the terminated Option. (It
                                           will expire earlier if your Service
                                           terminates, as described below.)
                                           IMPORTANT: If a properly executed
                                           "Notice of Exercise" form, together
                                           with payment for the exercise price
                                           and tax withholding, are not received
                                           by the Company prior to the
                                           expiration of the term of this
                                           Option, all rights to acquire Common
                                           Shares under this Agreement will be
                                           forfeited.

REGULAR TERMINATION                        If your Service terminates for any
                                           reason except death or Disability,
                                           your Option will expire at the close
                                           of business at Company headquarters
                                           on the 90th day after your
                                           termination date. During such 90-day
                                           period, you may exercise that
                                           portion of your Option that was
                                           vested on your Service termination
                                           date.

DEATH                                      If you die while in Service, your
                                           Option will expire at the close of
                                           business at Company headquarters on
                                           the date 12 months after the date of
                                           death. During that 12-month period,
                                           your beneficiary, estate or heirs may
                                           exercise that portion of your Option
                                           that was vested on your date of
                                           death.

DISABILITY                                 If your Service terminates because of
                                           your Disability, your Option will
                                           expire at the close of business at
                                           Company headquarters on the date 12
                                           months after your Service termination
                                           date. During such 12-


                                       4
<PAGE>   5

                                           month period, you or your legal
                                           guardian may exercise that portion
                                           of your Option that was vested on
                                           your date of Disability.

                                           "Disability" means that you are
                                           unable to engage in any substantial
                                           gainful activity by reason of any
                                           medically determinable physical or
                                           mental impairment which can be
                                           expected to result in death or which
                                           has lasted or can be expected to last
                                           for a continuous period of not less
                                           than 12 months, as determined
                                           pursuant to Section 22(e)(3) of the
                                           Internal Revenue Code of 1986, as
                                           amended.

NOTICE OF EXERCISE                         When you wish to exercise this
                                           Option, you must notify the Committee
                                           by filing the proper "Notice of
                                           Exercise" form at the address given
                                           on the form together with payment of
                                           the Exercise Price and any required
                                           tax withholding, as described below.
                                           Your Notice of Exercise must specify
                                           how many Common Shares you wish to
                                           purchase and how your Common Shares
                                           should be registered (in your name
                                           only, in your and your spouse's names
                                           as community property or as joint
                                           tenants with right of survivorship or
                                           in a trust for your benefit, or in
                                           the name of a brokerage firm for your
                                           account as designated by you). The
                                           Notice of Exercise will be effective
                                           when it is received by the Committee.
                                           If someone else wants to exercise
                                           this Option after your death, or
                                           Disability, that person must prove
                                           to the Committee's satisfaction that
                                           he or she is entitled to do so.

FORM OF PAYMENT                            When you submit your Notice of
                                           Exercise, you must include payment of
                                           the Exercise Price for the Common
                                           Shares you are purchasing. Payment
                                           may be made in one (or a combination)
                                           of the following forms:

                                           -   Your personal check, a cashier's
                                               check or a money order.

                                           -   Common Shares which have already
                                               been owned by you for more than
                                               six months and which are
                                               surrendered to the Company. The
                                               value of the Common Shares,
                                               determined as of the effective
                                               date of the Option exercise, will
                                               be applied to the Exercise Price
                                               and tax withholding obligations.

                                           -   By delivery (on a form prescribed
                                               by the Committee) of an
                                               irrevocable direction to a
                                               securities broker to sell Common
                                               Shares and to deliver all or part
                                               of the sale proceeds to the
                                               Company in payment of the
                                               aggregate Exercise Price and tax
                                               withholding obligations.

                                           -   By the delivery (on a form
                                               prescribed by the Company) of an
                                               irrevocable direction to pledge
                                               Common Shares to a securities
                                               broker or lender approved by the
                                               Company, as security for a loan,
                                               and to deliver all or part of the
                                               loan proceeds to the Company in
                                               payment of all or part of the
                                               Exercise Price and any
                                               withholding



                                       5
<PAGE>   6
                                           taxes.

WITHHOLDING TAXES                          You will not be allowed to
                                           exercise this Option unless you make
                                           acceptable arrangements to pay any
                                           withholding or other taxes that may
                                           be due as a result of the option
                                           exercise or the sale of Common Shares
                                           acquired upon exercise of this
                                           Option.

RESTRICTIONS                               By signing this Agreement, you agree
ON EXERCISE                                not to sell any Common Shares at a
AND RESALE                                 time when prohibited by applicable
                                           laws, regulations or Company or
                                           underwriter trading policies. In
                                           connection with any underwritten
                                           public offering by the Company of its
                                           equity securities pursuant to an
                                           effective registration statement
                                           filed under the Securities Act, you
                                           agree not to sell, make any short
                                           sale of, loan, hypothecate, pledge,
                                           grant any option for the purchase of,
                                           or otherwise dispose or transfer for
                                           value or agree to engage in any of
                                           the foregoing transactions with
                                           respect to any Common Shares without
                                           the prior written consent of the
                                           Company or its underwriters, for such
                                           period of time after the effective
                                           date of such registration statement
                                           as may be requested by the Company or
                                           such underwriters.

                                           In order to enforce the provisions of
                                           this paragraph, the Company may
                                           impose stop-transfer instructions
                                           with respect to the Common Shares.

                                           In the event that the sale of Common
                                           Shares under the Plan is not
                                           registered under the Securities Act
                                           but an exemption is available that
                                           requires an investment representation
                                           or other representation, you shall
                                           represent and agree at the time of
                                           exercise that the Common Shares
                                           being acquired upon exercising this
                                           Option are being acquired for
                                           investment, and not with a view to
                                           the sale or distribution thereof,
                                           and shall make such other
                                           representations as are deemed
                                           necessary or appropriate by the
                                           Company and its counsel.

TRANSFER OF OPTION                         Prior to your death, only you or, in
                                           the event of your Disability, your
                                           legal guardian, may exercise this
                                           Option. You cannot transfer or assign
                                           this Option. For instance, you may
                                           not sell this Option or use it as
                                           security for a loan. If you attempt
                                           to do any of these things, this
                                           Option will immediately become
                                           invalid. You may, however, dispose of
                                           this Option by beneficiary
                                           designation or in your will.

                                           Regardless of any marital property
                                           settlement agreement, the Company is
                                           not obligated to honor a Notice of
                                           Exercise from your spouse or former
                                           spouse, nor is the Company obligated
                                           to recognize such individual's
                                           interest in your Option in any other
                                           way.


RETENTION RIGHTS                           This Agreement does not give you the
                                           right to be retained by the Company
                                           in any capacity.  The Company
                                           reserves the right to terminate your
                                           Service at any time and for any
                                           reason.


                                       6
<PAGE>   7

STOCKHOLDERS RIGHTS                        You, or your estate or heirs, have no
                                           rights as a stockholder of the
                                           Company until a certificate for the
                                           Common Shares acquired upon exercise
                                           of this Option has been issued. No
                                           adjustments are made for dividends or
                                           other rights if the applicable record
                                           date occurs before your stock
                                           certificate is issued, except as
                                           described in the Plan.

ADJUSTMENTS                                In the event of a stock split, a
                                           stock dividend or a similar change in
                                           the Common Shares, the number of
                                           Common Shares covered by this Option
                                           and the Exercise Price per share may
                                           be adjusted pursuant to the Plan.
                                           Your Option shall be subject to the
                                           terms of the agreement of merger,
                                           liquidation or reorganization in the
                                           event the Company is subject to such
                                           corporate activity.

LEGENDS                                    All certificates representing the
                                           Common Shares issued upon exercise
                                           of this Option shall have endorsed
                                           thereon any legends required by
                                           applicable law.

APPLICABLE LAW                             This Agreement will be interpreted
                                           and enforced under the laws of the
                                           State of Delaware (without regard to
                                           their choice of law provisions).

THE PLAN AND                               The text of the Plan is incorporated
OTHER AGREEMENTS                           in this Agreement by reference.
                                           Certain capitalized terms used in
                                           this Agreement are defined in the
                                           Plan.

                                           This Agreement and the Plan
                                           constitute the entire understanding
                                           between you and the Company
                                           regarding this Option. Any prior
                                           agreements, commitments or
                                           negotiations concerning this Option
                                           are superseded.

BY SIGNING THE COVER SHEET OF THIS AGREEMENT, YOU AGREE TO ALL OF THE TERMS AND
CONDITIONS DESCRIBED ABOVE AND IN THE PLAN.


                                       7