One of the key housing programs that helps low-income and other needy New Yorkers afford their apartments has been effectively cut off for thousands of families.

City officials announced Thursday that they had stopped issuing new federal rent subsidy vouchers and were terminating the vouchers of 3,000 families who had yet to fully use them. They said they were taking those steps because of federal budget cuts and an increased demand for the vouchers in today’s economy.

The city’s public housing agency, the New York City Housing Authority, typically gives out thousands of vouchers every year through the Section 8 program. Poor, elderly and disabled tenants who receive the vouchers live in private apartments and pay about 30 percent of their income toward rent, with federally funded vouchers making up the difference.

Agency officials said that the nearly 128,000 families currently on its Section 8 waiting list would remain there, but with a few exceptions no new vouchers would be given to them or anyone else in 2010 without additional federal financing. In addition, 3,018 families — those who had received vouchers but were searching for an apartment or had identified an apartment but not yet completed the process and moved in — would have their vouchers terminated.

Since May, the agency has limited vouchers to those in emergency situations, and has stopped giving them out to families who are not in crisis. As a result, a majority of the 3,018 voucher holders were in emergency situations, including those who had recently been homeless, victims of domestic violence and young people leaving foster care.

“It’s a difficult but unavoidable decision,” the authority’s chairman, John B. Rhea, said at a news conference on Thursday.

Mr. Rhea said a “perfect storm” of factors was to blame.

In 2008 and 2009, Congress and the Department of Housing and Urban Development instructed the agencies that administer Section 8 vouchers nationwide to use money in their reserves to fill shortfalls in federal financing. New York housing authority officials said they had anticipated a $10 million shortfall in 2009, but the amount turned out to be $58 million. “We didn’t know how large it would be,” Mr. Rhea said.

He also said the agency had already surpassed by 2,000 vouchers its annual allotment of 99,000.

The authority was working with city officials to provide alternative rental assistance for many of the 3,000 voucher holders. Robert V. Hess, commissioner of the city’s Department of Homeless Services, said his agency was working to extend a state supervised rental assistance program for hundreds of formerly homeless families who had their vouchers terminated. “We don’t think there’s any cause for alarm at this point,” he said.

None of the families who are currently in an apartment and receiving the Section 8 subsidy are affected, officials said.

Elected officials and advocates for low-income housing expressed outrage over the move and criticized the authority for failing to do enough to prevent 3,000 families from losing the vouchers they had been given.

“It is shocking that the New York City Housing Authority is breaking its word to over 3,000 Section 8 voucher holders,” said City Councilman Bill de Blasio, a Democrat from Brooklyn.

Steven Banks, the attorney in chief for the Legal Aid Society, said the agency’s actions would swell the city’s family shelter system.

The Manhattan borough president, Scott M. Stringer, called for members of the authority’s governing board to resign. “I have a hunch that we’re about to be dealing with ‘Vouchergate,’ which is why we need city legislative hearings immediately,” Mr. Stringer said.