Sounding a somber note, Mayor Bloomberg and the City Council announced a budget deal that provides new funding for schools, avoids tax hikes, and would increase overall spending only slightly.

The centerpiece of the $59.1 billion budget agreement, reached last night at City Hall, is the restoration of $129 million in cuts to schools that had been proposed by the mayor. Speaker Christine Quinn said the funding boost would protect classrooms from budget cuts.

Rather than sustain cuts that the Department of Education had said could have reached as much as $1 million for some schools, public schools will maintain their budgets as they were written this year for next year.

A proposal by council members to raise the city’s hotel tax was not included in the budget. Neither was an increase to the city’s property taxes. The budget does include a $400 property tax rebate for homeowners. It calls for cuts to all city agencies and raises spending by 1.6%, which is less than the projected annual rate of inflation, 2.7%.

Mr. Bloomberg cautioned that the city might have to revise its budget in the coming months if its financial picture takes a turn for the worse.

“If the economy continues to slow down in our city, in the way it has elsewhere and the way we are starting to see some indicators saying so, then, you know, we’ll just have to revisit all of these things,” he said. “We will balance our budget and stay within compliance of the law. We will keep the streets safe and the schools open and our workforce able to focus on doing their job.”

Among other budget restorations touted by the council was an additional $18 million for the New York City Housing Authority, beyond what the mayor had proposed in his executive budget in May. Ms. Quinn also said the council is reducing the $50 million pot of money it distributes at its own discretion by about 8% to 10%.

The teachers union greeted the agreement as a success, offering a “big thank-you” to Ms. Quinn and praising Mr. Bloomberg, whom the union president, Randi Weingarten, had been criticizing for weeks.

The budget deal does not specify any additional Department of Education cuts. It does include a commitment to reducing class sizes, and it outlines two new programs that address areas activists have targeted — middle schools and programs for students learning English as a second language.

A parent advocate, Ann Kjellberg, said she is pleased that the City Council restored some funding, but said she was not sure $129 million is enough. She and other parent activists have been calling for the Department of Education to cut from its own budget to preserve schools.

The budget agreement, which council members are expected to pass Sunday, came only a few days before a July 1 deadline and was one of the most contentious in recent years. Earlier in the day, the mayor had described negotiations as “hard-fought.”

Both he and Ms. Quinn almost walked away from the rotunda without a handshake after their announcement, but an aide to the speaker shuffled over toward the mayor’s side of City Hall to ask if Mr. Bloomberg would return. The two posed for photos and exchanged a kiss on the cheek.