“It’s a number that’s been growing over a period of time,” Mr. Bratton said. “It’s reached a tipping point, however, I think, to use that term, that it did become more visible this summer.”

In addition to those living in shelters, there are 3,000 to 4,000 people living on city streets — the unsheltered homeless whom Mr. Bratton called “service-resistant.” About 40 percent of them are estimated to have significant emotional issues, he said. An additional 2 percent, he said, “scare the heck out of everybody,” and are those who typically attract complaints of irrational or violent behavior.

Officers with extra training are now moving through about 80 encampments across the city that have so far been identified, offering shelter to anyone in need, Mr. Bratton said. But he cited legal limitations. Begging, for instance, is constitutionally protected, he said. Aggressively begging, particularly within 10 feet of a bank’s A.T.M., or setting up an encampment, he said, are not.

“The begging,” he said, “if it is not intimidating, if it is not creating fear, that it is something that — those people you see sitting on the sidewalk with a sign: ‘Hungry. Need help.’ — that there is no legal way that we can deal with that person unless they are creating fear or intimidation of passers-by.”

Laura Mascuch, the executive director of the Supportive Housing Network of New York and member of the Campaign 4 NY/NY Housing, credited Mr. Bratton on Wednesday with calling attention to the need for more resources.