NEW YORK—American International Group Inc. on Monday began the sale of its remaining 9.2 million common shares of Transatlantic Holdings Inc.'s in a secondary offering.

AIG, which announced the sale on Friday, said the 9.2 million shares account for about 13.8% of Transatlantic's common shares. AIG subsidiary American Home Assurance Co. owns the shares, which analysts have said could bring AIG up to $500 million.

The closeout of AIG's stake in Transatlantic follows last June's secondary public offering of 29.9 million common shares of the reinsurer that brought AIG approximately $1.1 billion.

AIG said its offering Monday is concurrent with Transatlantic's addition to the S&P Midcap 400 Index.

Transatlantic, which said it plans to buy 2 million of the common shares, also said it expects to incur between $60 million and $90 million of first-quarter net catastrophe losses as a result of the earthquake in Chile and Windstorm Xynthia in Europe.