Mayor Bloomberg and his schools chancellor, Joel Klein, made their case for no-strings-attached state financing yesterday to the panel charged with making recommendations to carry out the decision in a historic education lawsuit.

During a hearing at Fordham Law School in Manhattan, Mr. Bloomberg said the city was not in a position to shoulder any additional financial burden unless it reduced services in other areas, such as after-school programs or police operations.

“We send millions of dollars more to Albany than we get back,” the mayor testified in a third-floor room used for sessions of moot court.

In addition, he said the state has the advantage of generating needed revenue over a much larger tax base.

He also said Governor Pataki’s proposed “state office of educational accountability” would create a more bureaucratic, dysfunctional system and would undermine mayoral control of the school system, which was granted two years ago.

“I don’t think you can make a good case that we need another level of accountability or oversight. If anything, I would argue that we have too much now,” Mr. Bloomberg said in response to questioning from the city’s head lawyer, Michael Cardozo. Adding deadlines and pressures from another regulatory body would misdirect resources, he said.

Five proposals have been advanced on how money should be added to the city’s budget to comply with a ruling of the state Court of Appeals in a lawsuit filed against the state by the Campaign for Fiscal Equity. The competing proposals come from the state Senate, the Assembly, the mayor, the governor, and the CFE.

The three-member panel of “special masters” was appointed by Justice Leland DeGrasse of State Supreme Court. It has until Nov. 30 to issue recommendations on how best to rework the state’s formula for distributing education money to municipalities, to ensure a “sound, basic education” for all children in the city’s public schools.

Mr. Klein, who was peppered with more questions, echoed the mayor’s points, saying the city was “systemically shortchanged.” He said the city would expand summer school programs, ramp up recruiting in the early grades, and improve middle and high schools, as part of a four-pronged plan previously outlined.

The mayor’s plan called for $5.3 billion in state money to satisfy the ruling in the lawsuit. Each of the other four plans calls for the city to shoulder a different portion of the burden.

The head attorney for the campaign, Michael Rebell, said yesterday the city had made a compelling case against another accountability office but said there needs to be a better vehicle for parents and teachers to influence decisions on education spending.

“The one place where we are a little concerned that things are not working as well as they should is getting the buy-in from the teachers and the parents,” Mr. Rebell said. “There is a strong sense of alienation from the teachers and the parents. Now is the time to have some more dialogue.”