Prudential of Britain said Monday that it had agreed to buy American International Group’s life insurance business in Asia in a deal valued at $35.5 billion.

The sale of American International Assurance, which is based in Hong Kong and is commonly known as A.I.A., would lead to the biggest repayment yet toward the more than $180 billion that the U.S. government has invested in A.I.G. as part of a huge series of bailouts. The Federal Reserve Bank of New York, which holds preferred shares in A.I.A., would receive the first $16 billion in proceeds from a sale.

With a takeover of A.I.A., Prudential would become the indisputable leader in Asia. Prudential said the combined group would be the leading life insurer in Hong Kong, Singapore, Malaysia, Indonesia, Vietnam, Thailand and the Philippines and the leading foreign life insurance business in China and India.

A 162-year-old company — which is not related to Prudential Financial in the United States — the British Prudential already draws a large part of its revenue from Asia, with more than 11 million policyholders in 13 markets.