WASHINGTON – The Obama administration on Tuesday estimated that the $700 billion financial bailout fund would cost taxpayers $51 billion – and possibly 43 percent less if the government succeeds in recouping the money it put into insurer American International Group Inc.

In a report issued two days after the formal end of the Troubled Asset Relief Program, the Treasury Department said that it still expected to incur “substantial losses” from the separate government seizure of housing giants Fannie Mae and Freddie Mac.

But even with those bailouts, the department reiterated its estimate that the cost of all the government’s bailout initiatives stemming from the 2008 financial crisis would cost less than 1 percent of the nation’s annual economic output.

In the savings and loan debacle of the late 1980s and early 1990s, the government spent about 2.4 percent of U.S. economic output, or gross domestic product, to rescue the industry, the Treasury said.

Throughout the report, Treasury touted its TARP program as being effective in unfreezing the markets for credit and capital and restoring confidence in the financial system.

“TARP undoubtedly helped to stem the financial panic in the fall of 2008 and contributed to the stabilization of the financial system,” Treasury Secretary Timothy F. Geithner wrote to lawmakers in submitting the report, which looks back on the two years since TARP was enacted.

Major projected losses from TARP include $17 billion from about $80 billion spent to rescue General Motors Co., Chrysler and their financing arms. The government’s mortgage modification program, which offers cash incentives to banks to rework home loans to avoid foreclosures, is expected to lose $46 billion.

Those and other losses would be partly offset by a projected profit of $16 billion on capital injections into banks.

Treasury’s powers under the law expired on Sunday. The law passed in October 2008 with support from lawmakers in both parties and the Bush administration.

The report is being circulated four weeks before the midterm elections. The economy has emerged as the top issue for voters, and many lawmakers could be punished for supporting the financial bailout.

Critics say it insulated banks from risky moves that nearly wrecked the economy and solidified permanently the dominance of a few large banks. And there was little help for Americans outside the world of high finance, they say.

Geithner acknowledged some missteps during a town hall meeting with TARP staffers last month.

“TARP was not perfect,” he said. But the program “delivered in ways few could have imagined.”

The new Treasury estimate is less than the $66 billion loss projected in August by the nonpartisan Congressional Budget Office and takes into account last week’s agreement between the government and AIG on a plan to recoup all taxpayer funds.

The plan involves Treasury converting preferred shares purchased with TARP money into common stock and selling them over time.

Based on AIG’s closing stock price Friday, that investment would give Treasury a $21.9 billion profit, which the report said would reduce TARP losses to $29 billion.