The budget is expected to be passed on Tuesday by the full 51-member City Council, although it is expected to garner more than a dozen “no” votes, split between council members who oppose cutting police funding at a time when crime is rising and those who think the police cuts do not go far enough.

Councilman Ben Kallos, a Democrat who represents the Upper East Side, said he planned to vote no on the budget, in part because he said the police cuts were insufficient.

“It is worse than it was before,” Mr. Kallos said in an interview.

“We are not seeing a meaningful reduction in head count and the changes that people are literally marching in the streets for,” he said. “I don’t think anyone marching for Black Lives Matter is doing it to see school safety agents moved from the N.Y.P.D. budget to the schools budget.”