After losing about 5,300 public school teachers to budget cuts over the last several years and watching class sizes rise, New York City plans to reverse course and add some teachers this fall, Mayor Michael R. Bloomberg announced on Thursday.

But the big impact under Mr. Bloomberg’s plan will be felt by principals, who will have more money to replace teachers who leave during the year as well as many lost to attrition in the current school year. As a result, 2,570 open teaching positions that would otherwise have been left open will now be filled.

Since 2009, the city’s schools have weathered five rounds of budget cuts, reducing the pool of teachers to 73,982 from about 79,300, according to the city’s estimates.

Earlier this year, the mayor’s preliminary budget projected a loss of roughly 1,100 teachers for the next academic year through attrition, leading City Council members to complain about the effect on class sizes, particularly for the youngest students.

At his budget presentation on Thursday, Mr. Bloomberg said the city would not go through with the cuts. Instead, he plans to spend about $185 million to replace the teachers who leave the schools this year, as well as some of those who left before.

“The good news is the number of teachers in our schools will rise next year,” Mr. Bloomberg said. “We’ve made up for some of the attrition of the teachers from this past year and into next year.”

Principals are still bound by the hiring freeze instituted in spring 2009 under Joel I. Klein, the chancellor at the time, as the city was reeling from the financial crisis; the hiring freeze required principals to fill vacancies from the current teaching pool. But since it began, the Department of Education has lifted some of the restrictions, which now exclude special education, English as a second language and some science teachers, among others.

City officials would not say whether they plan to relax the restrictions even further for next year.

A majority of the new teachers hired next year will work with special education students, city officials said, a response to an increase in the number of students with diagnoses of learning disabilities.

While some of the new teachers will work in classrooms that mix general and special education students — lowering the student-to-teacher ratio for all students — others will lead very small classes composed entirely of students with learning disabilities.

It is unclear how much the new hiring will affect class sizes citywide, which have risen steadily. In the last three years, the number of elementary school students in classes of 30 or more has tripled, according to a report by Councilman Brad Lander.

Mr. Bloomberg said he was also dropping plans to cut per-session spending — money the city pays teachers to work overtime to run student clubs and sports teams. This will cost the city roughly $30 million in next year, officials said.

But that does not mean that every school will be able to keep its after-school programs. Included in the mayor’s proposed budget are cuts to the Out-of-School-Time program, which is run by the Department of Youth and Community Development and finances about 420 programs citywide. For the next year, the city will award new contracts to only 220 programs.

The mayor also plans to reduce spending for child care programs, an annual threat and one that service providers and other elected officials have been protesting for months.

“We’ll see how all of that works out,” Mr. Bloomberg said at his budget presentation, noting that the details of the final budget have to be negotiated with the City Council. A budget is supposed to be approved before July 1. In the past, the Council has restored some funding for child care and after-school programs.

Shortly after the mayor spoke, Council Speaker Christine C. Quinn, a likely mayoral candidate, said she was “optimistic” that the cuts to child care and after-school programs could be mitigated.

Mr. Bloomberg used his budget presentation to admonish the city’s teachers’ union for not reaching an agreement with city officials on a new teacher evaluation system. If there is no deal by January, the city could lose $300 million in state aid.

“In order to receive these funds, the United Federation of Teachers has to come back to the bargaining table in a serious way and agree on the final details of this new evaluation system,” he said, adding that the city and the union have already worked out the bulk of their differences and there is “no substantive reason” for drawn-out negotiations.

The union’s president, Michael Mulgrew, said it was not the union, but the city that walked away from teacher evaluation talks in late December.

“The U.F.T. went to Albany to fight for better teacher evaluations, and we will continue to work toward a system that works for the students and teachers of New York,” he said in a statement.

Mr. Mulgrew nevertheless described the proposed budget as “good news.”

“New York City has lost thousands of teachers over the last few years and it’s good news to hear that we will be adding educators to the system,” Mr. Mulgrew said. “I can’t thank the City Council enough for making education a priority.”