<PAGE>   1
 
   AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON FEBRUARY 2, 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:
 

<TABLE>
<S>                                             <C>
[ ]  Preliminary Proxy Statement                [ ]  Confidential, for Use of the Commission
                                                Only (as permitted by Rule 14A-6(e)(2))
[ ]  Definitive Proxy Statement
[ ]  Definitive Additional Materials
[X]  Soliciting Material Pursuant to Section 240.14a-11(c) or Section 240.14a-12
</TABLE>

 
                     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 the 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:
 
        ------------------------------------------------------------------------
 
     (4)  Date Filed:
 
        ------------------------------------------------------------------------

<PAGE>   2
                            [AIG LOGO] AMERICAN INTERNATIONAL GROUP, INC.
                                       70 Pine Street New York, New York 10270
NEWS

Contact: Ned Burke
         Assistant Manager, Public Relations
         212/770-3141

                AIG GRANTED EARLY TERMINATION OF HART-SCOTT-
           RODINO WAITING PERIOD ON AMERICAN BANKERS ACQUISITION


NEW YORK, February 2, 1998 -- American International Group, Inc. (AIG) has
announced that it has been granted early termination of the waiting period
under the Hart-Scott-Rodino Antitrust Improvements Act of 1976 with respect
to its pending acquisition of American Bankers Insurance Group, Inc. (American
Bankers). The early termination, which was effective on January 30, 1998, also
applies to the option to acquire 19.9 percent of American Bankers common stock
at $47.00 per share.

                                 #     #     #

        American International Group, Inc. (AIG) may solicit proxies in favor
of the acquisition of American Bankers Insurance Group, Inc. (American Bankers)
by AIG. The participants in this solicitation may include AIG, the directors of
AIG (M. Bernard Aidinoff, Lloyd M. Bentsen, Pei-yuan Chia, Marshall A. Cohen,
Barber B. Conable, Jr., Martin S. Feldstein, Leslie L. Gonda, Evan G. Greenberg,
M.R. Greenberg, Carla A. Hills, Frank J. Hoenemeyer, Edward E. Matthews, Dean
P. Phypers, Howard I. Smith, Thomas R. Tizzio, Edmund S.W. Tse and Frank G.
Wisner) and the following executive officers and employees of AIG: Edmund J.
Burke (Assistant Manager, Public Relations); Florence A. Davis (Vice President
and General Counsel); William N. Dooley (Vice President and Treasurer);
Charlene M. Hamrah (Director of Investor Relations); Joseph M. Norton, Jr.
(Director of Public Relations); David Przywara (Assistant Director of Investor
Relations); John T. Wooster, Jr. (Vice President, Communications) and Louis F.
Zearo (Vice President and Deputy Comptroller). Certain of the directors of AIG
are also executive officers of AIG. AIG may contact holders of shares of
American Bankers preferred stock and common stock by mail, telephone,
facsimile, telegraph, the Internet, newspapers or other publications of general
distribution and personal interviews. AIG will bear the expenses of any
solicitation made by AIG.

        As of the date of this communication, AIG has no interest, direct or
indirect, in any securities of American Bankers, except that AIG has given
notice of its intent to exercise an option to purchase up to 19.9% of the
outstanding shares of American Bankers common stock, which option was
previously granted to AIG by American Bankers. Such option and AIG's exercise
thereof are more fully described in a Schedule 13D that AIG has filed with the
Securities and Exchange Commission.

        Other than as set forth above, as of the date of this communication,
none of AIG or, to the knowledge of AIG, any of the persons listed above, has
any security holdings in American Bankers.


                                 #     #     #


       AIG is the leading U.S.-based international insurance organization and
among the largest underwriters of commercial and industrial insurance in the
United States. Its member companies write property, casualty, marine, life and
financial services insurance in approximately 130 countries and jurisdictions,
and are engaged in a range of financial services businesses. American
International Group, Inc.'s common stock is listed on the New York Stock
Exchange, as well as the stock exchanges in London, Paris, Switzerland and
Tokyo.


                                 #     #     #