<PAGE>

                                                                    EXHIBIT 10.4

                TERMINATION OF REMARKETING AGREEMENT relating to
                  6.15% Reset Put Securities ("REPS") Due 2033
                                       of
                            Cox Communications, Inc.

         This Agreement, dated as of June 25, 2003, is by and between COX
COMMUNICATIONS, INC., a Delaware corporation (the "Company"), and MORGAN STANLEY
& CO. INCORPORATED, a Delaware corporation ("MS").

         WHEREAS, the Company has issued $250,000,000 aggregate principal amount
of its 6.15% REset Put Securities due 2033 (the "Notes");

         WHEREAS, as more particularly set forth in the Remarketing Agreement
dated as July 27, 1998 by and between the Company and MS (the "Remarketing
Agreement"). MS has the option to elect to purchase and remarket the Notes in
whole, but not in part (such right being referred in this Agreement as the
"Remarketing Option") in its capacity as the Remarketing Dealer (as defined in
the Remarketing Agreement);

         WHEREAS, the Company, wishes to terminate MS's Remarketing Option on
the terms and conditions set forth herein; and

         WHEREAS, the Company and MS wish to terminate the Remarketing
Agreement:

         NOW, THEREFORE, for good and valuable consideration, the receipt and
adequacy of which are hereby acknowledged, the Company and MS hereby agree as
follows:

         1.       The Company and MS agree to terminate MS's Remarketing Option
under the terms hereof. Such termination shall become effective on the date that
is the earlier of (i) the date on which the Company terminates MS's Remarketing
Option with respect to all of the Notes or (ii) July 29, 2003 (the "Termination
Date"). The Remarketing Agreement shall be terminated in its entirety as of the
Termination Date and, other than as provided in Section 8 thereof, no provision
thereof or rights or obligations thereunder shall survive such termination. The
Company agrees to repurchase the entire principal amount of the Notes on the
Coupon Reset Date (as defined in the Remarketing Agreement) at a price equal to
100% of the principal amount of the Notes plus accrued and unpaid interest, if
any, on the Notes to but excluding the Coupon Reset Date.

         2.       The Company may elect at any time and on multiple days during
the Termination Period (as defined herein), but not later than the Termination
Date, to terminate MS's Remarketing Option with respect to all or any portion of
the Notes by providing notice to MS on any such day specifying the aggregate
principal amount of the Notes with respect to which the Remarketing Option is
being terminated. Any remaining portion of the Notes with respect to which the
Company has not terminated MS's

<PAGE>

Remarketing Option during the Termination Period shall be deemed terminated as
of the Termination Date. For purposes hereof, "Termination Period" shall mean
any New York Business Day commencing on the date hereof up to and including the
Termination Date. A "New York Business Day" shall mean any day on which
commercial banks are open for business in New York.

         3.       In consideration for the early termination of the Remarketing
Option respecting all or any portion of the aggregate principal amount of the
Notes, the Company agrees to pay MS such amounts as shall be agreed between the
Company and MS during the Termination Period. Such consideration shall be agreed
between the Company and MS promptly after MS's receipt of each notice by the
Company of its election to so terminate. Upon agreeing consideration for each
such termination, the parties hereto shall complete and sign the Confirmation of
Unwind in the form attached hereto as Annex A and deliver such Confirmation of
Unwind to each other.

         4.       Any notice to terminate all or a portion of the Remarketing
Option that is received by MS during the Termination Period by 11:00 a.m., New
York time, shall be effective as of the date such notice is received, and the
Remarketing Option respecting the portion of the aggregate principal amount of
the Notes stated therein shall be terminated as of such date. Any notices
received by MS during the Termination Period after 11:00 a.m., New York time,
shall be deemed effective on the New York Business Day following the date
received. Consideration for the portion of the Remarketing Option that is
terminated shall be due and payable prior to the close of business on the
effective date of such termination.

         5.       Any notice or other communication required to be given
hereunder shall be given in accordance with Section 10 of the Remarketing
Agreement, provided that notice under Section 2 of this Agreement may be
communicated through electronic mail subject to telephone confirmation of
receipt.

         6.       This Agreement shall be governed by, and construed and
enforced in accordance with, the laws of the State of New York applicable to
contracts made or to be performed in such state without reference to the choice
of law doctrine.

         7.       This Agreement may be executed in several counterparts, each
of which will be regarded as an original and all of which will constitute one
and the same document.

                                        2

<PAGE>

         IN WITNESS WHEREOF, this Agreement has been entered into as of the 25th
day of June 2003.

                                 COX COMMUNICATIONS, INC.

                                 By: /s/ Jimmy W. Hayes
                                     -----------------------------
                                     Name: Jimmy W. Hayes
                                     Title: Executive Vice President, Finance
                                            and Chief Financial Officer

                                 MORGAN STANLEY & CO. INCORPORATED

                                 By: /s/ William C. Thum
                                     -----------------------------
                                     Name: William C. Thum
                                     Title: Vice President

<PAGE>

                                                                      Appendix A

<TABLE>
<CAPTION>
                Aggregate Principal                      Remaining
                Amount Subject to                       Outstanding
Unwind Date          Unwind           Consideration   Principal Amount
----------------------------------------------------------------------
<S>             <C>                   <C>             <C>
6/25/03           $250,000,000         $ 10,458,891     $200,000,000
6/26/03           $200,000,000         $  4,707,373     $175,000,000
6/27/03           $175,000,000         $  4,316,055     $150,000,000
7/2/03            $150,000,000         $  8,635,012     $100,000,000
7/3/03            $100,000,000         $  4,100,276     $ 75,000,000
7/7/03            $ 75,000,000         $  7,852,196     $ 25,000,000
7/8/03            $ 25,000,000         $  3,663,110     $          0
----------------------------------------------------------------------
Total                                  $ 43,732,913
</TABLE>

                                      COX COMMUNICATIONS, INC.

                                      By: /s/ Jimmy W. Hayes
                                          -------------------------------------
                                      Name: Jimmy W. Hayes
                                      Title: Executive Vice President, Finance
                                             and Chief Financial Officer

                                      MORGAN STANLEY & CO. INCORPORATED

                                      By: /s/ William C. Thum
                                          -------------------------------------
                                          Name: William C. Thum
                                          Title: Vice President