* Government has incentive to continue support - Moody's

* Go-slow restructuring preserves value - Moody's

* AIG shares up 3.7 pct (Adds stock and CDS price moves)

NEW YORK, Nov 10 (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: Quote, Profile, Research), 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 [ID:nN06174086]

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