NEW YORK (Reuters) - Insurance giant AIG has made progress on its restructuring and will likely be able to repay a taxpayer bailout and buy back much of the government's stake in the company, Moody's Investors Service said on Monday.

The Moody's statement was a rare expression of optimism for American International Group Inc <AIG.N>, which has received up to $180 billion of federal aid and is now 80 percent owned by U.S. taxpayers.

Moody's said AIG's restructuring plan still relies heavily on government support, but if its operations and global financial markets continue to stabilize, the company likely can generate enough value to repay the government.

The vote of confidence sent AIG's hard-hit shares up 3.7 percent to $37.52. The cost of insuring $10 million of AIG debt for five year fell to around $732,000 annually, down $10,000 from Monday, according to Markit Intraday.

AIG posted its second straight quarterly profit last week, helped by a recovery in the value of its investments. But its underlying business remained weak. For details click on

The quarterly results "show continued stabilization of the core insurance operations despite challenging market conditions," Moody's said.

With the government likely to recoup its investment, it has incentive to continue supporting AIG and its various creditors, Moody's said. The agency affirmed AIG's long-term credit rating of A3, the seventh-highest investment grade, with a "negative" outlook.

Credit spreads on AIG's 8.25 percent notes due in 2018 tightened by 0.15 percentage point on Tuesday, to 7.51 points over U.S. Treasuries, according to MarketAxess.

AIG's $180 billion of federal aid includes more than $80 billion in loans. The company has sought to sell major business units to help repay the government, but has struggled to find buyers willing to pay enough.

Since the appointment of former MetLife Chief Executive Robert Benmosche as AIG CEO in August, the company has focused on rebuilding the value of some businesses previously slated for sale, Moody's said.

"We believe that the slower approach to restructuring could help AIG to generate more favorable values from its business portfolio than would be the case under rushed asset sales," it said.

(Reporting by Dena Aubin; Additional reporting by Joe Giannone and Karen Brettell; editing by Walker Simon and John Wallace)