In a conference call with reporters, the department’s secretary, Shaun Donovan, said the one-night snapshot showed a “remarkable” drop in national homeless numbers in recent years given the economic downturn. He credited the collaboration among 19 federal agencies in tackling the problem.

But the story is different in New York and Los Angeles, which showed large increases in homelessness.

In New York, where the shelter population has reached levels not seen since the Depression era, the count in January estimated 64,060 homeless people in shelters and on the street in January 2013, or 13 percent more than in January 2012. Among large cities, only Los Angeles had a larger percentage increase. Its homeless population rose by 27 percent, although its total of 53,798 was lower than New York’s.

Federal officials said the increases were driven by a rise in families who could no longer pay their rent, a problem that is more acute in areas where affordable housing is scarce and rents are especially high. The group of very poor renters who pay more than half their income in rent and are struggling to hold onto their homes has grown by 43 percent nationwide since 2007, housing officials said.

Across the country, nearly a quarter of all homeless people, 23 percent, are under 18.

The administration of Mayor Michael R. Bloomberg set out to make a significant dent in homelessness with an overhaul of policies in the mid-2000s. But instead, the city’s shelters are packed, with more than 50,000 people relying on them. Mr. de Blasio has promised to reverse course by restoring the preference given to homeless families for a portion of public housing apartments and rental subsidies. He has also vowed to negotiate with the state and HUD to create a new rent subsidy program.