Mayor Bloomberg stopped short of declaring victory in his fight with Albany for school aid, despite the billions of dollars in funding now expected to flow to the city to build new public schools.

While Mr. Bloomberg praised the deal reached by the state Legislature that authorizes $11.2 billion in money for capital expenses over the next five years, he characterized it as “an important step” in a larger fight.

“I don’t know that I should declare victory until we can look each other in the eye and say that every child in this city gets a quality education,” he said.

The deal, which has not yet been backed by Governor Pataki, caps an ongoing battle over school funding in which Mr. Bloomberg has, in the last several months, traded in his more staid strategy for hardball tactics to get the money. In the last eight weeks, he has indicated that he would back candidates to take on state senators who were not on board with the city’s funding requests and announced that the city would halt 21 school construction projects if it did not receive more education money from Albany.

“His tactic paid off,” the director of the Empire Center for New York State Policy, an arm of the Manhattan Institute, E.J. McMahon, said. “I’m not saying I like the results, but the strategy worked.”

The budget deal addresses the city’s capital spending with a combination of $6.5 billion in state money and the rest from the city, over five years. But the deal earmarks only a small fraction of the operating money. That number is about $400 million, a fraction of the $4.7 billion to $5.6 billion in operating money the court ordered in its ruling on a lawsuit filed by the Campaign for Fiscal Equity, which started the fight for more schools funding. Mr. Bloomberg, who in the past has cited the lawsuit to condemn Albany lawmakers, distanced himself slightly yesterday.

“That’s a lawsuit brought by some private citizens,” he said. “I testified in favor of the suit, we filed a brief in favor of the suit. But that’s a separate issue … I’ve got to do something today.”

The president of the United Federation of Teachers, Randi Weingarten, called the budget deal a “huge step forward,” but said the next step is to get the full funding. The executive director of the CFE, Geri Palast, said the same and added that the organization would “most likely” be back in court if that doesn’t happen.