Apparently, $18 billion worth of American International Group shares weren’t enough for investors.

The Treasury Department said on Tuesday that it had sold an additional $2.7 billion worth of its holdings in the bailed-out insurance giant, as underwriters for the offering exercised what’s known as an overallotment option to meet higher-than-expected demand.

At $20.7 billion, the offering is the single-biggest sale of Treasury’s holdings in A.I.G. to date.

The banks running the stock sale priced the shares on Monday night at $32.50, which is above the $28.73 that the government says is its break-even price on its investment.

The expanded offering means that the federal government’s stake in A.I.G. has now fallen to about 15.9 percent, down from 53 percent before the stock sale. As recently as April of 2011, the Treasury Department held a 92 percent stake in the financial firm.

The department added in a statement that it and the Federal Reserve Bank of New York had recovered about $197.4 billion from their collective rescue of A.I.G. in the depths of the financial crisis in 2008, pulling in more than the $182 billion that the government had made available for the bailout. But that calculation includes the cancellation of roughly $50 billion in potential aid that was never doled out.

Investors appeared little moved by the news of the offering’s terms on Tuesday. Shares in A.I.G. were nearly flat in late trading, at $33.31, though they had fallen 2 percent on Monday in anticipation of the Treasury Department’s forthcoming sale.