In a statement on Monday, the Treasury said it launched an underwritten public offering for its remaining 234.2 million shares of common stock.
At Monday's closing prices the stake would be worth some $7.81 billion. Treasury said that the sale would be jointly led by Bank of America Merrill Lynch, Citigroup, Deutsche Bank, Goldman Sachs and JPMorgan.
Treasury also said it would continue to hold warrants to buy common stock even after the share offering is complete.
In September 2008 AIG was rescued minutes before it would have been forced to file for bankruptcy protection. The bailout ultimately totaled $182 billion.
At one time the government estimated it would never recover all of those funds, but as AIG restructured and returned to viability it was able to repay the entire rescue plus generate a profit for taxpayers.
(Reporting by Timothy Ahmann in Washington and Ben Berkowitz in Boston; Editing by Phil Berlowitz)