American International Group's financial health is showing signs of improvement because of the billions of dollars in taxpayer funds used to bail out the ailing insurer, a government watchdog agency said on Thursday.

Overall, federal assistance appears to be facilitating a more orderly restructuring of the company, the Government Accountability Office said in a report.

The GAO, the investigative arm of Congress, said AIG's insurance operations have exhibited recovery since its last report in April 2010, but it added that federal assistance has been a critical factor.

AIG, which received $182 billion in assistance from the New York Federal Reserve Bank and the U.S. Treasury, recapitalized last week and repaid the Fed. Now the U.S. government is AIG's majority owner with a 92 percent stake.

In its third report on the bailout of AIG, the GAO said U.S. taxpayers' risk exposure to the insurer increasingly is expected to be tied to the success of AIG and its value as seen by investors in the company's common stock.

The government's ability to fully recoup the federal assistance will be determined by the long-term health of AIG, the report said.

A Treasury official said taxpayers were in a strong position to recover every dollar put into AIG.

AIG has already paid back the Federal Reserve and taxpayers are next in line to recoup their stake in the company, Treasury's acting Assistant Secretary Tim Massad said in a statement.

(Reporting by Rachelle Younglai; Editing by Andrew Hay)