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


The Federal Housing Finance Agency said it had concluded after months of study that debt forgiveness might benefit up to half a million homeowners, but that the costs — including the cost to taxpayers — outweighed the potential benefits.


Offering debt forgiveness “would not make a meaningful improvement in reducing foreclosures in a cost-effective way for taxpayers,” the agency’s acting director, Edward J. DeMarco, said in a statement.


“The choices we’ve had to make are hard but they need to be made,” he told reporters.


The decision is a direct rebuff to the Obama administration, which has pressed Mr. DeMarco for more than a year to reconsider his longstanding opposition. It is also a blow to the administration’s efforts to increase help for homeowners.


The Treasury Department emphasized Tuesday that Mr. DeMarco had the “sole legal authority” to make the decision, but it released a letter to Mr. DeMarco from Treasury Secretary Timothy F. Geithner asking the agency to reconsider.


“I do not believe it is the best decision for the country,” Mr. Geithner wrote.


 The decision also is likely to infuriate Congressional Democrats, who have pressed for a debt forgiveness program. Republicans have supported Mr. DeMarco’s refusals.


 Mr. DeMarco did announce Tuesday two other changes sought by the Obama administration. He said that Fannie and Freddie would offer lower-cost refinancings to a broader universe of borrowers. The agency also will seek to encourage new lending by addressing concerns that lenders will be forced to absorb the cost of defaults on loans purchased by Fannie and Freddie. Federal Reserve officials have said that such a change is a crucial step to increase the benefits of lower interest rates for borrowers.


The Obama administration initially shared Mr. DeMarco’s opposition to principal reduction, arguing as he does now that the government should focus on other, less costly means of helping homeowners. But since 2010, the government has offered incentives to private mortgage companies to offer principal reduction to some troubled borrowers.


In January, the administration said that it would sharply increase the amount of those incentives, partly to induce the participation of Fannie and Freddie.


The housing agency is charged by Congress with minimizing the cost of bailing out the two companies, which were seized in 2008. The administration said it would cover the cost of debt forgiveness from a separate pot of money, the $700 billion that Congress allocated in 2008 to bail out the financial system. Administration officials argued that this would allow the housing agency to meet its statutory responsibility.


In rejecting debt forgiveness on Tuesday, Mr. DeMarco also rejected this argument.


He said that he interpreted his mandate as requiring a minimization of the total cost to taxpayers, and that the administration’s plan did not change that math.


The housing agency’s analysis showed that roughly 500,000 borrowers would be eligible for debt forgiveness, although it noted that no more than half were likely to participate. Even on that basis, the agency found that taxpayers could save $500 million because aid recipients would be more likely to continue making mortgage payments.


But the agency concluded that the likely pool of beneficiaries was even smaller, based on participation in existing programs. Moreover, it estimated that executing the plan would impose significant costs on Fannie Mae and Freddie Mac.


And Mr. DeMarco also referred to the agency’s abiding concern that offering debt forgiveness would encourage borrowers to default in hopes of a better deal.


There has been little indication that the broad availability of debt forgiveness to borrowers whose loans are owned by private companies has caused such a problem. But Mr. DeMarco said the risks would be greater for Fannie and Freddie because, he argued, such a program would be more comprehensive and better publicized.


The agency’s analysis is unlikely to appease its critics.


Mr. DeMarco said Tuesday that the program could have benefits for taxpayers, but he argued that those benefits were uncertain and that there were additional costs beyond the numbers, like potential disincentives to future lending.


Mr. DeMarco also said that the agency did not consider whether lower levels of debt might bolster economic growth. Economists have long argued that this is a primary reason for the government to support debt reduction.


That has fueled criticism that the agency is seeking reasons to reject principal forgiveness even if the program appears to meet the requirements of the law.


“I just don’t understand why they’re applying this level of caution and scrutiny,” said Jared Bernstein, a former economic adviser to Vice President Joseph R. Biden Jr. “It strikes me as bad for homeowners, bad for taxpayers and bad for the macroeconomy.”