American International Group Inc., the largest commercial insurer in the U.S. and Canada, said it may repurchase as much as an additional $2 billion of common stock after selling its aircraft-leasing business.

The insurer has bought back about $418 million of shares since the end of the first quarter, according to a statement today from the New York-based company. It has $2.12 billion remaining on its share-repurchase authorization.

AIG sold International Lease Finance Corp. to AerCap Holdings NV last month for $3 billion in cash and about $4.6 billion in AerCap stock. The insurer got rid of about $26 billion of liabilities in the deal.

The ILFC sale “and our strong capital position have allowed us to authorize this share repurchase, which enables us to return a portion of our sale proceeds directly to our shareholders,” AIG Chairman Robert S. Miller said in the statement.

AIG shares were little changed today at $54.95 in New York. They have gained 7.6 percent this year, beating the 5 percent advance of the Standard and Poor’s 500 Index.