New York City has greater budgetary priorities than hiring 1,000 more police officers, including fixes for failing schools, dysfunctional jails and increasing homelessness, Mayor Bill de Blasio said Friday.

De Blasio laid out his most detailed case yet against boosting the NYPD's numbers while answering New Yorkers' radio listener calls -- a first for his mayoralty -- on WNYC's "Brian Lehrer Show."

"There are so many other challenges," de Blasio told Danny of Rockaway Park, who urged the mayor to add 1,000 cops to his $78.3 billion budget, which is due June 30.

De Blasio said the NYPD's success at keeping crime near historic lows during his 17 months in office is "a reason to stick with what we're doing." So is fiscal prudence, he said.

De Blasio took four calls during the 37-minute radio appearance -- three from Queens and one from Manhattan.

Unlike most of his recent predecessors, de Blasio had until yesterday shied away from forums where he can hear unfiltered feedback from constituents, such as call-in shows or town-hall-style meetings. Some community leaders have complained about the lack of such access. A spokeswoman for the mayor didn't return messages asking whether he was turning over a new leaf.

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During the interview, de Blasio hinted at progress toward a deal resolving a dispute with Gov. Andrew M. Cuomo over the balance of developer and union interests to promote affordable housing in a real estate tax break known as 421-a. "I've spoken to the governor several times," he said.

He urged the renewal and strengthening of rent regulations ("There are some people playing with fire in Albany right now") and disputed contentions that reducing the NYPD's stop-and-frisk practice has led to a crime spike.

De Blasio said that although shootings and murders are up in some precincts year-to-date compared with the same period last year, overall crime is down, and he was certain the NYPD would cool down the hot spots. He noted that the city saw a similar spike around this time last year, and the NYPD addressed the problem with existing manpower.

The mayor also said police are freed up to do more effective policing now that they have reduced the use of stop-and-frisk encounters and low-level marijuana arrests.

The City Council and Police Commissioner William Bratton have called for increasing the current 35,000 head count. De Blasio listed other needs.

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"We've got a school system that needs real work, that has profound problems that are not resolved. We have the problems at Rikers Island that are not resolved. We have the homeless problem that has unfortunately grown to unacceptable proportions in recent years," de Blasio said.

The homeless population in the city's shelters is near 57,000, and the city is negotiating with the U.S. Justice Department to reform a jail system federal prosecutors say suffers from "a deep-seated culture of violence."

Separately, de Blasio praised Democratic presidential contender Hillary Rodham Clinton's call Thursday for expanding voting rights but stuck to his no-endorsement stance while awaiting details on how she would tackle income inequality.