WASHINGTON — The independent federal agency that administers Fannie Mae and Freddie Mac said on Tuesday that it would not let the mortgage companies offer debt forgiveness to borrowers, again rejecting the entreaties of the Obama administration.


The Federal Housing Finance Agency said it had concluded after months of study that up to half a million homeowners could benefit from such a program, and that taxpayers might save $1 billion because aid recipients would be more likely to continue making mortgage payments.


But the agency’s acting director, Edward J. DeMarco, said the benefits most likely would be much smaller — too small in his judgment to offset potential costs, including the risk that some borrowers would stop making payments in pursuit of a better deal.


Offering debt forgiveness “would not make a meaningful improvement in reducing foreclosures in a cost-effective way for taxpayers,” Mr. DeMarco said in a statement Tuesday.


The announcement is a direct rebuff to the Obama administration, which has pressed Mr. DeMarco for more than a year to let Fannie Mae and Freddie Mac join nearly every other major mortgage company in offering debt forgiveness to borrowers who owe more than the value of their homes.


On Tuesday, the Treasury Department immediately called for the agency to reconsider. “I do not believe it is the best decision for the country,” Timothy F. Geithner, the secretary, wrote in a public letter to Mr. DeMarco.


The decision also infuriated Congressional Democrats, while Republicans rallied to the agency’s defense.


“The administration put incredible political pressure on Director DeMarco, and he deserves praise for standing up for the best interests of the American people,” said Representative Spencer Bachus, an Alabama Republican who is chairman of the House committee that oversees the agency.


The importance of debt forgiveness in preventing foreclosures and reviving economic growth has been a contentious issue since the start of the housing crisis six years ago.


Research shows that borrowers whose mortgage debts exceed the value of their homes on average are less likely to keep making payments. Some economists also argue that high levels of debt are impeding consumer spending, the nation’s primary economic activity.


But debt forgiveness is more expensive than other methods of reducing a borrower’s payments, like deferring a portion of the debt or reducing the interest rate, in part because the lender is forgoing the chance to benefit if housing prices recover.


Moreover, as the generosity of aid increases, so does the incentive to seek help.


And there is a final consideration that weighed heavily in the analysis that the housing agency published Tuesday: After years of debate, many borrowers have slipped beyond the reach of help. The agency noted that most of the half-million homeowners it counted as candidates for debt forgiveness had not made a mortgage payment in more than a year.


The agency estimated that 74,000 to 248,000 borrowers might successfully obtain a debt reduction. In the best case, it estimated that Fannie Mae and Freddie Mac could collect another $500 million in mortgage payments. But it cautioned that the low end of the range was more likely, resulting in a much smaller financial benefit.


And it noted that the entire benefit could be erased if as few as 3,000 borrowers decided to stop making payments in the hopes of qualifying for debt forgiveness.


“The projected impact,” Mr. DeMarco told reporters, “could be negative for taxpayers or it could be positive, depending on the assumptions.” But given his assessment of the costs, he said, it was clearly not large enough.


In reaching this conclusion, Mr. DeMarco flatly rejected the administration’s efforts to change his longstanding opposition by offering to pay the bill.


The housing agency is charged by Congress with minimizing the cost of bailing out Fannie and Freddie, which were seized by the government in 2008 to preserve their role as the primary source of financing for new mortgage loans.


The administration’s mortgage modification program offers incentives to lenders who forgive a portion of the borrower’s debt, and in January, the White House tripled the incentive as direct inducement to Mr. DeMarco.


The agency said Tuesday that the companies could reap $2.7 billion, increasing the total savings from debt forgiveness to as much as $3.6 billion.


But Mr. DeMarco in effect rejected the administration’s helping hand, insisting Tuesday that the only important number was the total cost to taxpayers.


The details of the analysis did little to assuage the agency’s critics, who noted the agency’s math still seemed to suggest that taxpayers could benefit.


“It is incomprehensible that Mr. DeMarco would reject the chance to save up to a billion dollars in taxpayer funds while helping nearly half a million homeowners stay in their homes,” said Representative Elijah E. Cummings, Democrat of Maryland.


Analysts also see little evidence that existing incentives for principal reduction have lured borrowers to default, although Mr. DeMarco said he feared that a high publicized announcement by Fannie and Freddie might produce a different result.


The agency also sketched some proposals on Tuesday that it said would benefit homeowners. One potentially significant change could encourage mortgage companies to loosen lending standards by limiting their responsibility if they sold the loans to Fannie and Freddie — the standard method of raising money for more loans — and the borrower eventually defaulted. Federal Reserve officials have said that the current standards significantly impede the availability of loans. The agency said that a new standard would be published by September.