American International Group Inc will transfer its troublesome asbestos risk to Berkshire Hathaway Inc , relieving it of a book of business that has cost it billions of dollars, the bailed-out insurer said on Wednesday.

Laying off that risk to Berkshire's National Indemnity unit lets AIG trade a large one-time fee for the safety of knowing it will not face more huge charges -- a plus as the U.S. government tries to convince investors to take its 92 percent stake in the company.

AIG is paying $1.65 billion to Berkshire to take on the U.S.-based risk in exchange for a coverage limit of $3.5 billion. Any further exposure beyond that limit would come back to AIG.

As the fee is less than the reserve for asbestos exposure AIG is still carrying on its books, the company will recognize a deferred gain over time on the difference.

AIG took a charge of more than $4 billion in the fourth quarter because its exposure to years-old asbestos claims in its Chartis property and casualty insurance business was much higher than it had expected.

National Indemnity has become a partner of choice for insurers looking to limit their asbestos exposure in exchange for hefty up-front fees. Last July CNA Financial Corp did a similar deal for a $2 billion payment. National Indemnity also did a similar but larger deal with a Lloyd's of London affiliate in 2006.

Barclays Capital, in a note, said the deal is attractive for Berkshire because of the investment income it can generate on the fee.

AIG shares rose 1.1 percent to $32.48 in afternoon trading, while Berkshire's actively traded Class B shares were up 1.3 percent at $81.53. The Standard & Poor's insurance index<.GSPINSC> rose 1.3 percent.

AIG shares closed Tuesday at their lowest point in nearly seven months. Adjusting for a dividend of warrants in early January, the stock has lost a third of its value this year, sharply underperforming a roughly flat S&P insurance index.

The shares have been falling closer to the government's break-even point, which is $28.72 per share. At Tuesday's closing price, the government's potential profit stands at just over $5.6 billion.

(Reporting by Ben Berkowitz; Editing by Gerald E. McCormick and Matthew Lewis)