Some of the 10,000 low-income families in danger of losing the rental assistance they get through a voucher program will probably keep receiving it, thanks to $23.5 million that the New York City Housing Authority is to receive from the federal government, officials said Thursday.

The money, from the federal Department of Housing and Urban Development, will help bridge a $45 million budget gap in the authority's rental-voucher assistance program.

The housing authority had said it might have to cut assistance for up to 10,000 lower-income families in the program, known as Section 8, because of the budget gap. The authority did not estimate on Thursday how many families could still lose their vouchers if no additional financing came through.

In a statement, John B. Rhea, the housing authority's chairman, described the allocation as "an enormous help," but he said the problem was still severe.

"We still must find other sources of money to reduce the $21 million-plus deficit that remains, and we are aggressively pursuing other options to financially stabilize the program," Mr. Rhea said.

The HUD money is coming from $150 million that Congress set aside to assist housing authorities with their voucher programs. New York City's housing authority, the country's largest, got the most money, said Sandra Henriquez, an assistant secretary at HUD. She said the City of Los Angeles received $10 million, the second largest amount.

"We wanted to make sure as many housing authorities as possible who qualified for the money at least got something," Ms. Henriquez said.

Residents with Section 8 vouchers usually pay 30 percent of their income in rent to a private landlord, and the voucher pays the rest. In New York, about 102,000 families have vouchers, which the housing authority administers.

HUD stipulates the maximum number of vouchers that housing authorities can use. Much of the New York housing authority's deficit was caused because the agency exceeded that cap. The agency continued issuing vouchers until December, even though HUD had warned the authority in May that it was concerned it would exceed the assigned amount.

Ms. Henriquez said the department had "not established a good set of penalties at all" for authorities that exceeded the cap.

Housing policy experts welcomed news of the federal financing.

"Clearly Nycha had run its reserves almost down to nothing and was facing a shortfall," said Douglas Rice, a senior policy analyst at the Center on Budget and Policy Priorities in Washington. "A lot of families would've been hurt without a significant amount of additional funding."

About 1,000 housing agencies applied for the financing, and 600 received money, said Donna White, a HUD spokeswoman. The beneficiaries were determined by which housing authorities needed the money the most, she said, though few agencies got the full amount requested, including New York, which had asked for $35 million.