<PAGE>   1
 
   AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON JANUARY 30, 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)
 
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: Joe Norton
         Director of Public Relations
         212/770-3144

             AIG REGISTRATION STATEMENT RELATING TO ACQUISITION OF
           AMERICAN BANKERS INSURANCE GROUP, INC. DECLARED EFFECTIVE


NEW YORK, January 30, 1998 -- American International Group, Inc. (AIG) has
announced that its Registration Statement filed in connection with AIG's
pending acquisition of American Bankers Insurance Group, Inc. (American
Bankers) has been today declared effective by the Securities and Exchange
Commission.

        A proxy statement/prospectus will be mailed to American Bankers
shareholders on Monday, February 2, 1998. The special meeting for holders of
American Bankers Preferred Stock will be held on March 4, 1998, and the special
meeting for holders of American Bankers Common Stock will be held on March 6,
1998. Shareholders of record on January 30, 1998 will be entitled to vote at the
special meetings.

                                 #     #     #

        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.

        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.


                                 #     #     #