Reuters

The government continues to unwind its stake in American International Group, as the insurer slowly recovers from the depths of the financial crisis.

The Treasury Department announced on Sunday that it would sell 163,934,426 shares of A.I.G. at $30.50 apiece. The $5 billion stock sale is expected to reduce the government’s stake in the company to 63 percent from 70 percent.

A.I.G. plans to buy back around $2 billion of the stock. In March, when the Treasury sold $6 billion of A.I.G. shares at $29 apiece, A.I.G. bought back $3 billion worth of shares.

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“We’re continuing to make significant progress exiting our investment in A.I.G.,” Timothy G. Massad, the assistant secretary for financial stability, said in a statement. “We remain hopeful that taxpayers will ultimately recover every single dollar invested in the company, which is something few would have expected during the depths of the financial crisis.”

The sale is the latest effort by the government to unwind its holdings in A.I.G. In 2008, the government undertook a huge bailout of the insurer, eventually providing $182 billion in aid. After the current offering, the government said its total investment related to A.I.G. would stand at $39 billion.

The government is taking advantage of the rebound in A.I.G.’s stock. Its shares are up more than 40 percent since the beginning of the year, closing at $32.83 on Friday. In premarket trading on Monday, A.I.G. stock stood at $30.52, roughly in line with the offering price. The Treasury considers its break-even price is $28.73.

Many of the insurer’s old assets are also finding new homes. The Federal Reserve Bank of New York has been steadily selling mortgage-backed bonds and other assets that were taken from A.I.G.’s portfolio into special vehicles, called Maiden Lane II and Maiden Lane III, as part of the bailout. This year, the New York Fed has sold bonds with a face value of billions of dollars to banks including Goldman Sachs, Credit Suisse, Barclays and Deutsche Bank Securities.

As it did in stock sales, A.I.G. bought back some of those bonds for its own balance sheet. In February, it said it had purchased “just under” $2 billion in face value from the Maiden Lane II portfolio.