The report continued: “Even among borrowers who receive five-year modifications, some will eventually fall behind on their payments and once again face foreclosure. In the final reckoning, the goal itself seems small in comparison to the magnitude of the problem.”

The Treasury took issue with the report and said the pace of modifications was picking up. The number of active permanent modifications in March was 227,922, an increase of 35 percent from those in February. An additional 108,212 permanent modifications are awaiting borrower approval.

Shaun Donovan, secretary of Housing and Urban Development, said in an interview that those were the important numbers to focus on.

“One percent of these loans defaulting is a tiny fraction,” Mr. Donovan said. “Given how stressed these borrowers are, even in the best situation, there will be redefaults. But I don’t think there is any evidence that would cause us to worry at this point.”

Julia R. Gordon, senior policy counsel for the Center for Responsible Lending in Washington, said she expected the number of post-modification defaults to continue to rise.

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“It’s definitely alarming to look at those statistics,” she said. “The current model for modifications doesn’t necessarily produce sustainable results.”

While the program is too new to predict its long-term success, the data on previous modification efforts is not encouraging.

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Sixty percent of modifications undertaken by banks in late 2008 were in default a year later, according to the latest Mortgage Metrics Report compiled by the Office of Thrift Supervision and the comptroller of the currency.

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Many of these private plans either kept the payments the same or increased them. Inevitably, those mortgages suffered the highest failure rate: about two-thirds of the borrowers defaulted again.

Loans for which the payments were decreased by at least 20 percent failed at a slower but still significant rate of about 40 percent.

The government program takes a more aggressive approach, lowering the interest rates for all loans. On many loans, terms are also extended or principal payments put off for years. Treasury data shows that the median savings for borrowers receiving permanent modifications is $512 a month.

Many borrowers remain deeply indebted, however. They owe not only on the house, but on homeowner association fees, home equity loans, car loans, alimony and credit card interest.

Even after modification, $61 out of every $100 earned by the borrower goes to servicing debt, government figures show. For increasing numbers of modification recipients, mortgage relief is apparently not enough to stave off financial collapse.

“If you can help 60 percent, and 40 percent have to fall back, is that worthwhile?” asked John Courson, president of the Mortgage Bankers Association. “Clearly for the 60 percent it was, and the 40 percent weren’t going to make it anyway.”

The Treasury said on Wednesday that it had always anticipated that some homeowners would not sustain a modification, which was one reason the program had been greatly expanded. New elements focus on allowing distressed homeowners to sell their properties for less than they owe and on shaving the principal owed by borrowers.

The notion of cutting principal, however, has already run into some resistance from the big banks, which do not want borrowers to get the idea that their mortgage can be chopped on a whim.