Mayor Bill de Blasio, who for months said New York City couldn't afford to expand the police force, voiced confidence Tuesday that there will be enough money to pay for 1,300 more NYPD officers under a budget deal struck with the City Council.

Savings to be found by placing civilians in administrative jobs now performed police -- and by limiting overtime costs -- helped persuade him, and Commissioner William Bratton's case for more cops proved "compelling," de Blasio said at an unrelated event in Queens.

"We found options to go much further on civilianization . . . much further on the cap on overtime," the mayor said. "And that was a crucial factor to me in this decision."

The council had asked earlier this year for 1,000 new officers. Just a few weeks ago, de Blasio had said no head count hike was needed.

The 1,297 added officers -- with 300 dedicated to anti-terrorism work -- would cost $170 million, offset by $70 million in savings with the civilianization of 415 positions and the overtime cap, the mayor said.

Pensions, health care and other fringe costs would add up to another $38 million for the fiscal year beginning July 1, mayoral spokeswoman Amy Spitalnick said yesterday.

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Benefit costs for a bigger police force are "quite a heavy lift," said Maria Doulis of the watchdog Citizens Budget Commission.

Pensions, health care, a salary boost as the Patrolmen's Benevolent Association works out a new contract and the possible restoration of disability benefits under debate in the city and in Albany will add up, Doulis said.

"All these things are uncertain and unsettled, but would impact the cost of both immediately and for the long term," she said.

NYPD overtime is expected to cost $550 million this year. The cap will be set at $513 million next year and the $454 million every year after that, Spitalnick said.

But City Councilwoman Elizabeth Crowley (D-Queens) said overtime may not be "something you can control" because of unforeseen needs. She pointed out that pension benefits increase with the amount of overtime worked.

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If the overtime reductions are not achieved, the NYPD will be required to find the savings elsewhere, Spitalnick said.

She said a projection of the lifetime cost of the new officers is not part of the financial plan.

The new hires would bring the NYPD's head count to about 35,800 by July 1, 2016.

Independent Budget Office spokesman Doug Turetsky said adding new cops would be cheaper than in years past because of adjustments to the pension tier for newer officers and health care savings negotiated in union contracts.

The staffing level could also shrink through attrition in future years when the city may have less cash, he said.

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Bratton, who had openly lobbied to expand the force, said Tuesday he learned of de Blasio's change of heart when the mayor and Council Speaker Melissa Mark-Viverito shook hands in City Hall's rotunda on the budget deal Monday night.

De Blasio also insisted there was no epiphany.

"There was not, like, a light shone down from the heavens," he said. Meetings with Bratton in recent weeks went from a "broader discussion of his vision to a much more detailed one that became very, very compelling to me," he said.

Bratton said, "These were very intense collaborative discussions."With Anthony M. DeStefano