The City Council speaker, Christine Quinn, yesterday offered what observers said was a “restrained” set of proposed initiatives and used her first major policy address to call for an end to a city budget process that council members have long derided as a “dance” with the mayor.

In its official response to Mayor Bloomberg’s $52.2 billion preliminary budget, the council proposed $84.5 million in new initiatives and restoring cuts of $338 million. Ms. Quinn delivered the response in a formal 30-minute speech before an audience of close to 400 packed into the council chambers at City Hall.

The council’s most ambitious initiatives focused on early childhood education and small businesses. In a move lauded by the United Federation of Teachers, Ms. Quinn proposed spending $135 million over three years to extend the city’s entire pre-kindergarten program to full-day services. Currently, 34,000 children attend half-day programs and 7,000 are enrolled for a full school day.

The council also is proposing $154 million in tax cuts, including $70 million in credits for small businesses and $84 million for low-income families.

Ms. Quinn’s speech contained no direct criticism of Mr. Bloomberg or his administration, and in both her formal address and later comments to reporters she sought to continue the spirit of cooperation that has marked her relationship with Mr. Bloomberg in the three months since her election as speaker.

“We’ve had a very cooperative working relationship between the council and the Bloomberg administration so far, and I anticipate that that cooperation will continue as we move through the budget process,” Ms. Quinn told reporters after her speech.

A spokesman for Mr. Bloomberg, Jordan Barowitz, said the administration was “reviewing the speaker’s proposals and we look forward to working with the council throughout the budget process.”

Ms. Quinn’s comments also struck a notably different tone from that of her predecessor, Gifford Miller, who threatened to have the council pass its own budget during last year’s negotiations, which came as he was running to unseat Mr. Bloomberg. (Mr. Miller returned to City Hall yesterday, praising Ms. Quinn for a “terrific speech.”)

Council members and observers characterized Ms. Quinn’s limited set of spending and restoration proposals as part of a strategy to “extend her hand” to Mr. Bloomberg in the hopes that he will agree to what is perhaps the council’s top priority – a reform of the budget process.

“It’s better to light a candle than to curse the darkness,” a council member of Queens, Eric Gioia, said.

The executive director of the watchdog group Citizens Union, Richard Dadey, said Ms. Quinn had proposed initiatives that “make it easy” for the mayor to support. “It was not your typical laundry list of demands,” Mr. Dadey said. The speaker “was clear about not posturing in a way that other speakers have in the past.”

The council’s official budget response comes in the middle of a five-month process that began with Mr. Bloomberg’s offering of his preliminary budget in February and must by law end with a balanced budget on July 1. Ms. Quinn leveled her most pointed rhetoric at that practice, which annually features an executive budget laden with cuts that the council then seeks to restore.

“The list of cuts changes a little bit from one year to the next and the amount swings with the city’s economic fortunes,” Ms. Quinn said. “But the roles and the steps are the same year after year after year. The whole thing feels a lot like that movie ‘Groundhog Day.'”

Ms. Quinn proposed changing the process so that the administration and the council work together to evaluate programs and how they should be funded.

A professor of public policy at Baruch College, Douglas Muzzio, praised Ms. Quinn’s speech but said there was a limit to how much she could succeed in changing the budget procedure.

“You’re not going to fundamentally alter the relationship between the council and the mayor,” Mr. Muzzio said.

Among the council’s other proposals were $17.1 million in restored funding for the city’s district attorney’s offices, $1 million for an expansion to the city’s 311 hotline to train education specialists to answer parents’ questions, and about $340,000 to fund nutrition and anti-hunger initiatives. The council had earlier announced proposals to spend $9.9 million on bulletproof vests for police officers and $11.66 million to bolster services aimed at preventing child abuse and neglect.

Ms. Quinn gained her biggest laugh in announcing the funding for the district attorney’s offices, quoting verbatim the famed opening of the TV show “Law & Order”: “In the criminal justice system, the people are represented by two separate yet equally important groups. …”