<PAGE>   1
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MARCH 3, 1998
 
                            SCHEDULE 14A INFORMATION
 
          PROXY STATEMENT PURSUANT TO SECTION 14(a) OF THE SECURITIES
                              EXCHANGE ACT OF 1934
 
Filed by the Registrant [ ]
 
Filed by a Party other than the Registrant [X]
 
Check the appropriate box:
 
[ ]  Preliminary Proxy Statement    [ ] Confidential, for use of the Commission
[ ]  Definitive Proxy Statement     Only (as permitted by Rule 14A-6(e)(2))
[x]  Definitive Additional Materials
[ ]  Soliciting Material Pursuant to Section 248.14a-11(c) or Section 240.14a-12
                   
                    AMERICAN BANKERS INSURANCE GROUP, INC.
- --------------------------------------------------------------------------------
                (Name of Registrant as Specified in Its Charter)

                      AMERICAN INTERNATIONAL GROUP, INC.
- --------------------------------------------------------------------------------
    (Name of Person(s) Filing Proxy Statement if other than the Registrant)
 
Payment of Filing Fee (Check the appropriate box):
 
[x]  No fee required. 

[ ]  Fee computed on table below per Exchange Act Rules 14a-6(i)(4) and 0-11:
 
     (1)  Title of each class of securities to which transaction applies:
 
 
     (2)  Aggregate number of securities to which transaction applies:
 
 
     (3)  Per unit price or other underlying value of transaction computed
          pursuant to Exchange Act Rule 0-11 (Set forth the amount on which the
          filing fee is calculated and state how it was determined):
 
 
     (4)  Proposed maximum aggregate value of transaction:
 
 
     (5)  Total fee paid:

[ ]  Fee paid previously with preliminary materials.

[ ]  Check box if any part of the fee is offset as provided by Exchange Act Rule
     0-11(a)(2) and identify the filing for which the offsetting fee was paid
     previously. Identify the previous filing by registration statement number,
     or the Form or Schedule and the date of its filing.
 
     (1)  Amount Previously Paid:
 
        ------------------------------------------------------------------------
 
     (2)  Form, Schedule or Registration Statement No.:
 
        ------------------------------------------------------------------------
 
     (3)  Filing Party:
 
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     (4)  Date Filed:
 
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<PAGE>   2
        On February 27, 1998, American International Group, Inc. submitted 
the following letter to the New York Department of Insurance:

<PAGE>   3
               [AMERICAN INTERNATIONAL GROUP, INC. LETTERHEAD]


                                                        February 26, 1998


Mr. Marty Carus
Assistant Deputy Superintendent
   and Chief Examiner
Department of Insurance
State of New York
25 Beaver Street
New York, New York 10004

     Re:  Application of
          American International Group, Inc.
          to Acquire Control of
          American Bankers Insurance Group, Inc.

Dear Mr. Carus:

        I understand that counsel to Cendant has submitted to your Department a
letter arguing that AIG has already acquired control of ABIG by virtue of
contractual provisions of the merger and related agreements between AIG and
ABIG which AIG filed with your Department in its original Form A filing of
January 9, 1998.

        This argument is obviously wrong as a matter of fact and law and is
unworthy of your consideration. Cendant is simply attempting to confuse, delay
and abuse the regulatory process and the public securities markets by drawing
focus from the real issues--Cendant's unfitness to acquire an insurance company
and the illegality of Cendant's holding and voting proxies as to 10% or more
shares without prior approval.

        AIG does not control ABIG. The cited contractual provisions of the
merger agreement and related documents do not confer control as a matter of
fact or law.

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Provisions intended to facilitate the successful completion of a mutually
negotiated merger agreement are customary in merger agreements, as Cendant is
well aware. AIG has sought to obtain your Department's prior approval of its
acquisition of control of ABIG pursuant to the merger agreement and related
documents filed as part of AIG's Form A. In contrast, Cendant has failed to do
so with respect to its proxy solicitation.

        We appreciate the time and effort your Department is devoting to the
unfortunate situation caused by Cendant's hostile offer. Unlike Cendant, AIG
has not, and never will, ask your Department to devote your time and effort to
considering false and misleading arguments.


                                                Very truly yours,


                                                /s/ Florence A. Davis
                                                    Florence A. Davis

cc: Bonnie Steingart