9:01 p.m. | Updated

Taxpayers will soon shed their last holdings in the American International Group , more than four years after a rescue by the federal government during the most chaotic days of the financial crisis.

The Treasury Department said on Monday that it planned to sell all of its remaining 234.2 million shares, or 15.9 percent of the company, in a public offering. At current prices, that would raise more than $7.8 billion.

The stock sale, if completed, would realize a goal few dreamed possible in September 2008. As Lehman Brothers filed for bankruptcy, government officials scrambled to rescue A.I.G., an insurance giant that had become deeply intertwined with many Wall Street and European banks through its underwriting of credit-default swaps . The fear was that a collapse of the company could bring down the global financial system.

In the crisis, the government ended up extending lifelines to a number of financial institutions and to companies like General Motors . But it was the bailout of A.I.G. that resonated most deeply among the American public as a symbol of risk-taking and excess on Wall Street — and Washington’s complicity in it. At one point, the government had made more than $182 billion available to support A.I.G. Billions of that went to pay claims that the banks had on the insurer.

Public anger over the bailout prompted Congressional hearings, litigation, protests and widespread criticism from both the political left and the right.

Even Ben S. Bernanke , the Federal Reserve ’s chairman and one of the architects of the bailout, has said that the necessity of the plan made him angry. “We had no choice but to try to stabilize the system because of the implications that the failure would have had for the broad economic system,” he told a Senate panel in 2009.

At the time, critics feared that the company would be forced into a fire sale of assets to repay those loans, a sale that would deeply shortchange taxpayers.

Instead, the federal government has said that it expects to walk away from A.I.G. with a profit — about $15.1 billion to date, by the Treasury Department’s reckoning. That has followed both a steady stream of stock sales over the last two years and a resurgence in the insurer’s core operations.

“It’s gone way better than anyone expected in 2008 and 2009,” said Linus Wilson, an assistant professor of finance at the University of Louisiana at Lafayette. “People thought we’d put money down a dry hole and would never see it again.”

While the Treasury Department did not outline a timetable for its latest stock offering, the sale is expected to be completed quickly.

A spokesman for A.I.G., Jon Diat, declined to comment on the government’s plans, though he noted that the company did not plan to buy any of the Treasury Department’s shares in the offering.

The bailout left the federal government with a roughly 92 percent stake in A.I.G., a level of ownership that did not bode well for a recovery by the company.

Yet under Robert H. Benmosche, a strong-willed insurance executive who came out of retirement to lead A.I.G. in 2009, the company embarked on a more measured sale of assets aimed at maximizing sale prices. Mr. Benmosche repeatedly proclaimed that he would not accept cut-rate prices for the company’s assets, but stressed that under his watch, the insurer would become much more streamlined.

Shrinking the company to a more manageable size meant disassembling a disparate array of businesses built over decades by Maurice R. Greenberg , the former chief. Enormously valuable operations like the AIA Group and the American Life Insurance Company, two international life insurance units, were spun off or sold to raise cash.

Even that more measured approach drew criticism from Mr. Greenberg, who had repeatedly urged the government to devise a rescue plan that would keep his former company whole.

“Obviously it’s a good thing that A.I.G. is out of the government’s clutches,” the former chief said in an interview on Monday. “But it’s a different company now, and they had to sell off a great many treasures to do that.”

That campaign of asset sales has continued until as recently as this past weekend, when A.I.G. agreed to sell a majority stake in its enormous aircraft-leasing arm to a group of Chinese buyers for roughly $4.2 billion.

The insurer has focused on improving its remaining insurance operations. The company has steadily reported rising annual profits under Mr. Benmosche’s tenure, having earned $26.1 billion in the 12 months that ended Sept. 30.

Shares of the company have risen about 45 percent for the year to date.

Professor Wilson, who had criticized the government for not selling off its holdings in A.I.G. sooner, said on Monday that the Obama administration probably could have reaped a bigger profit. But he added that the rescue had achieved its main goal, while sparing taxpayers the pain of an ugly loss.

“I think it did stabilize the system,” he said. “The people who were the architects of the plan can be very pleased.”