<PAGE>   1
 
    AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MARCH 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
[X]  Definitive Additional Materials
[ ]  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
      On February 27, 1998, American International Group, Inc. submitted the
following letters to the Arizona Department of Insurance, the South Carolina
Department of Insurance and the Georgia Office of Insurance and Safety Fire
Commissioner, respectively:
        

                       [LOW & CHILDERS, P.C. LETTERHEAD]





                                                               February 27, 1998


VIA HAND-DELIVERY

Mr. John Greene
Director
Arizona Department of Insurance
2910 North 44th Street, Suite 210
Phoenix, Arizona 85018

      RE:  APPLICATION OF AMERICAN INTERNATIONAL GROUP, INC. TO ACQUIRE CONTROL
           OF AMERICAN BANKERS INSURANCE GROUP, INC.

Dear Director Greene:

      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. Provisions intended to facilitate the successful completion of a mutually
negotiated merger agreement are customary in merger agreements, as you (and
Cendant) are 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. AIG has not failed to seek
approval for another manner of acquisition of control of ABIG (as Cendant has
failed to do with respect to its proxy solicitation).



<PAGE>   3
Mr. John Greene
February 27, 1998
Page 2


     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/ Steven R. Henry
                                   ------------------------------
                                   Steven R. Henry


SRH:mal

cc:  Charles Cohen, Deputy Director
     S. David Childers, Esq.      

<PAGE>   4
            [SOWELL TODD LAFFITTE BEARD & WATSON, L.L.C. LETTERHEAD]


                               February 27, 1998


Gwendolyn L. Fuller, Esquire
South Carolina Department of Insurance
Post Office Box 100105
Columbia, SC 29202-3105

         RE:  Acquisition of American Bankers Insurance Group, Inc. by
              American International Group, Inc.
              Our File No.:  3645/1504

Dear Gwen:

I understand that counsel for Cendant has submitted to the Department a letter
dated February 24, 1998, 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 the Department in its original Form A
filing of January 9, 1998.

This argument is wrong as a matter of fact and law and is not worthy of
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. Provisions intended to facilitate the successful completion of a mutually
negotiated merger agreement are customary in merger agreements, as you (and
Cendant) are aware. AIG has sought to obtain the 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. AIG has not failed to seek approval for
another manner of acquisition of control of ABIG (as Cendant has failed to do
with respect to its proxy solicitation).

<PAGE>   5

                  [SOWELL TODD LAFFITTE BEARD & WATSON, L.L.C. LETTERHEAD]

Gwendolyn L. Fuller, Esquire
February 27, 1998
Page 2


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

                                   Very truly yours,

                                   /s/ Cal Watson
                                  
                                   J. Calhoun Watson

JCW:cln





<PAGE>   6
                [HUNTER, MACLEAN, EXLEY & DUNN, P.C. LETTERHEAD]

                               February 27, 1998

VIA HAND DELIVERY

The Honorable John Oxendine
Commissioner of Insurance
Office of Insurance and Safety Fire Commissioner
Suite 612, West Tower
2 Martin Luther King, Jr. Drive
Atlanta, GA 30334
Attention: Margaret Witten, Esq.

          RE: APPLICATION OF AMERICAN INTERNATIONAL GROUP, INC. TO ACQUIRE
              CONTROL OF AMERICAN BANKERS INSURANCE GROUP, INC.

Dear Commissioner Oxendine:

     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.

     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 matter of fact or law.
Provisions intended to facilitate the successful completion of a mutually
negotiated merger agreement are customary in merger agreements, as you (and
Cendant) are 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. AIG has not failed to seek
approval for another manner of acquisition of control of ABIG (as Cendant has
failed to do with respect to its proxy solicitation).

 

<PAGE>   7
                   [Hunter, Maclean, Exley & Dunn Letterhead]

The Honorable John Oxendine
February 27, 1998
Page 2

     We appreciate the time and effort your Department is devoting to the
unfortunate situation caused by Cendant's hostile offer. Please feel free to
call me if you have any questions or concerns with this or any other matter.



                                        Yours very truly,


                                        /s/ Todd M. Campbell     
                                        -------------------------------
                                            Todd M. Campbell



TMC/tsp