With handshakes and kisses, Mayor Bloomberg and the City Council speaker, Christine Quinn, sealed a deal for a $52.9 billion budget that includes more funding for public housing, full-day pre-kindergarten classes, and children’s protective services.

The budget, the first negotiated by Ms. Quinn, includes far less additional funding – $233 million – than the council requested for restored program cuts and new initiatives. The new speaker did achieve long-sought changes to the budget process, as Mr. Bloomberg agreed to annually fund five-day library service and an expansion of the city’s summer jobs program and trash collection services, thus eliminating the need for the council to fight for their inclusion in the budget each year.

Mr. Bloomberg and Ms. Quinn announced the budget accord shortly after 6 p.m. yesterday with nearly the entire council perched on the City Hall steps behind them. The outdoor venue broke with tradition, as budget agreements are usually announced in the rotunda of City Hall. The two leaders have forged a close working relationship since Ms. Quinn’s election as speaker in January, and both preached fiscal prudence in discussing what the mayor termed a “realistic and responsible” budget that, despite a $3.4 billion surplus, contained few major new initiatives.

“We are not only making investments; we are also practicing rigorous fiscal responsibility,” Mr. Bloomberg said. “We are not going to repeat the mistakes of the past and squander our current economic good fortune.”

Saying the council shared the mayor’s priorities, Ms. Quinn said lawmakers were “sending a clear message as an institution that we need to act as the stewards of taxpayer dollars.”

Among the new initiatives that made it through two weeks of negotiations were $7 million to convert 2,000 half-day pre-kindergarten slots to a full day; $6.2 million for additional protective services for children, and $20 million more for the New York City Housing Authority. The money for public housing comes in addition to the $100 million that the administration had proposed allocating to close a $168 million budget gap.

The budget also includes funding for 1,200 new police officers, $6.5 billion in capital funding for the city’s schools as part of a $13 billion deal passed by the state Legislature earlier this year, and a continuation of the $400 property tax rebate for homeowners.

Facing large budget gaps in 2008, 2009, and 2010, Mr. Bloomberg faced little resistance to his plan to spend most of the surplus to balance next year’s budget and fund a $2 billion health fund for retirees. Despite the high spirits yesterday, he again warned that “the good times aren’t going to be here forever.”

Administration and council officials finished negotiations yesterday amid the usual hustle and bustle of budget season at City Hall. Lobbyists and other advocates were camped on the building’s steps, and council committees held hearings throughout the day.

The deal struck yesterday ends what many viewed as Ms. Quinn’s first major test as speaker, both in her leadership of the council and in her relationship with Mr. Bloomberg.

The early reviews for her performance were largely positive, and council members applauded several times when initiatives were announced at yesterday’s ceremony.

“She did very well, in terms of leadership and participation,” a council member of Manhattan, Gale Brewer, said. Ms. Brewer said Ms. Quinn rightly sacrificed a higher dollar amount for concessions on altering the budget process, such as the annual funding for libraries, summer jobs, and trash collection.

The Republican leader of the council, James Oddo of Staten Island, said Ms. Quinn worked “effectively, tirelessly, and with a good sense of humor.”

Predictably, not all of the council 51 members were satisfied. Council Member Charles Barron of Brooklyn said the council should “have drawn a line in the sand with the mayor” to get more funding.

In the five months since the mayor released his preliminary budget, Ms. Quinn has sought to change how the council reviews and negotiates spending with the administration, as well as the process by which members propose their own budget initiatives.

Looking to avoid a repeat of council members asking for nearly $1 billion in new spending each year, the speaker rankled some lawmakers by limiting how many initiatives each could put forward and requiring proposals to have the endorsement of at least 10 members from across the city. After facing some resistance, Ms. Quinn compromised by giving an extra initiative to heads of committees, who make up more than half the council.

Absent from this year’s negotiations was the tension associated with the talks in 2005, when the council speaker, Gifford Miller, was in the midst of a bid to unseat Mr. Bloomberg as mayor. Mr. Miller tried unsuccessfully to vote down the mayor’s citywide trash plan, and the loss damaged his bargaining stance.

A balanced budget must be in place by June 30. The council is expected to vote either late today or tomorrow.