It was a multipart answer to a query about whether New York City homeless shelters were needlessly turning people away. But with his concluding line, Mayor Michael Bloomberg provoked a host of new questions and a deluge of criticism.

"Nobody's sleeping on the streets," Mr. Bloomberg said Tuesday at the tail end of a news conference.

In fact, more than 3,200 people were living on the streets in 2012 by the city's own count, and Mr. Bloomberg's comments may have unintentionally shined a light on their rising numbers.

By the afternoon, outraged homeless advocates and elected officials were calling the mayor out of touch. And New Yorkers expressed disbelief.

"He hasn't been to the Upper West Side, has he?" said Dawn Hilton, a 57-year-old nurse.

The 2012 count of homeless people on the street came last January and marked a 23% increase from 2011, according to the city. The year-over-year increase was particularly stark in Brooklyn, rising 52%, and in the Bronx, up 47%.

Mr. Bloomberg's remark came in response to a question about a new city policy that turns homeless families and children away from city shelters during freezing temperatures if officials determine they have an alternative place to sleep. Under the old policy, known as "Code Blue," the city would shelter families even if officials believed they had another housing option, when the temperature outside plummeted below freezing.

"The public does not want to—and should not have to—support somebody if they have alternatives," Mr. Bloomberg said Tuesday. "We want to make sure that our moneys are available to those who really don't have any alternatives. And, so, that's all we're trying to do—nobody's sleeping on the streets."

Later, when questioned whether the mayor stood by his comments, Samantha Levine, a spokeswoman, said the mayor's meaning was clear: The city's policy, "which, as usual, provides shelter to anyone who doesn't have a place to stay, is not resulting in anyone sleeping on the streets."

"Yes, Mr. Mayor, they are," replied Patrick Markee, a senior policy analyst at the Coalition for the Homeless, an advocacy group. "The city's cruel policy of turning away homeless families and children in subfreezing cold is dangerous and shameful, and will only add to those numbers."

Public Advocate Bill de Blasio, a Democrat running to succeed Mr. Bloomberg, called the mayor "either blind or willfully ignorant." "New Yorkers are sleeping on the street, in no small part because of his failed policies," he said.

The response renewed a familiar criticism of the city's billionaire mayor whose common touch has failed before, once telling snowed-in New Yorkers to see a Broadway show after a historic blizzard in 2010 and saying Con Edison deserved the city's gratitude during a 2006 blackout.

Mr. Bloomberg's record on homelessness is an area where even his aides acknowledge he has fallen short of his goals.

Mr. Bloomberg in 2004 said he would cut both the number of people who sleep on the streets and use the shelter system by two-thirds by 2009, but neither pledge has been fulfilled. Instead, the homeless shelter system population has surged to record levels. As of Friday, there were 48,737 homeless people in city shelters.

Barbara Brancaccio, a spokeswoman for the city's Department of Homeless Services, said all families are granted conditional shelter upon their initial application at the city's homeless intake center.

"For re-applicants, we take into account weather conditions, and we work to ensure that applicants who have alternate living situations do not take up beds that are needed by those who truly have no other recourse," she said.

Last week, a state appeals court unanimously affirmed a lower court's decision to block the Bloomberg administration from implementing a policy that would turn away single adults from shelters unless they demonstrate that they have no other housing options. City officials have said they are exploring their legal options.

New Yorkers were divided on Mr. Bloomberg's record on the homeless on Tuesday.

Howard Sichel, 59, said he sees far fewer homeless people than before former Mayor Rudy Giuliani took office. However, recently he said he has noticed more homeless people.

"I see people begging a lot," said Dr. Sichel, a chiropractor from Port Washington, N.Y., on Long Island. "I think it's desperation."

John Mendola, 53, was homeless for more than 40 years up until last month when he got an apartment in the Bronx thanks to an outreach program. "You tell Bloomberg to come down here," said Mr. Mendola, who still begs for money outside Penn Station. "There are a lot of people who sleep here."

—Alison Fox contributed to this article.