NEW YORK » The city is set to hire nearly 1,300 new police officers as part of its $78.5 billion budget agreement, honoring a proposal put forth by the City Council over Mayor Bill de Blasio’s initial objections.

The new officers will cost the city $170 million. The costs will be offset by $70 million in overtime savings. About 300 officers will be assigned to counterterrorism.

The hires were first reported by The Associated Press. They will join a force of about 35,000 uniformed officers, the nation’s largest.

The deal was made public and sealed with a handshake by de Blasio and City Council Speaker Melissa Mark-Viverito, Democrats, at City Hall late Monday.

Additionally, the budget authorizes the hiring of 400 administrative aides to take over desk jobs currently filled by police officers. Those officers will then be freed up to be deployed on the street for increased community policing.

A year ago, de Blasio flatly denied Mark-Viverito’s call to hire 1,000 new officers, pointing to record low crime rates and suggesting that the resources would be better used elsewhere to fulfill the mayor’s vision of a liberal, activist government that would better the lives of the less fortunate.

For much of the past year, City Hall stuck to that script. But police Commissioner William Bratton began intermittently advocating for the new hires, Mark-Viverito continued to push the plan as a way to improve outreach in neighborhoods often suspicious of police and pockets of the city suffered a surge in shooting and homicides in recent weeks.

Though overall crime is down 6.7 percent from this time a year ago, shootings and murders are up. Murders have risen from 138 to 154, 11 percent, through Sunday, while shootings have gone up from 488 to 515.

A total of 1,297 new officers will be hired. Many political observers expected that a compromise would be reached and the city would hire fewer than 1,000 officers because of eventual pension costs stemming from new hires. But administration officials said late Monday that the jump was partly due to Bratton’s ongoing efforts to revamp police department strategies; he is expected to announce several new initiatives later this week.

The entire budget will go to a vote before the full council, also later this week. The vote is expected to largely be a formality.

The issue of policing has always been a delicate one for de Blasio, who’s serving his first term as mayor.

He was elected on a campaign to improve relations between police and minorities, largely by curbing the overuse of stop and frisk, a tactic that allowed police to stop anyone deemed suspicious. Its critics, however, said it discriminated against black and Latino men.

With his push to reform the New York Police Department as a backdrop, de Blasio then faced an open revolt from the rank-and-file police union in the wake of the Eric Garner chokehold death. Though an uneasy truce took hold, the de Blasio team has been particularly wary of a rise in crime, knowing it could undermine the mayor’s agenda.