"When AIG will be able to pay the government completely back for its assistance is currently unknown because the federal government's exposure to AIG is increasingly tied to the future health of AIG, its restructuring efforts and its ongoing performance as more debt is exchanged for equity," Gene Dodaro, the acting comptroller general of the United States, wrote in a letter describing the GAO's findings.

Officials in the U.S. Treasury Department and at the Federal Reserve Board told GAO staffers that AIG must repay a Federal Reserve Bank of New York credit facility before the government's AIG trust can dispose of its AIG stock, Mr. Dodaro said.

AIG is supposed to repay the credit facility by Sept. 13, 2013.

Treasury officials and AIG trust trustees plan to coordinate their divestment efforts, Mr. Dodaro said.

The trustees of the AIG trust said they will begin working on an exit strategy when AIG has repaid the New York Fed, according to Mr. Dodaro.

At the Treasury Department, the "team that manages the AIG investment has been running scenarios of possible exit strategies but has not decided which strategy to employ," he said.

The AIG trust could convert its AIG Series C Preferred Stock into common stock and dispose of the common stock through a public offering or a private sale, Mr. Dodaro said.

The Treasury Department could dispose of its shares by having AIG redeem the shares; converting the shares into common stock and selling the stock through a public offering; or selling the shares to an institutional buyer or buyers through a private sale.