Mayor Bloomberg is initiating the biggest overhaul of the school system since he won control of it. His effort to devolve many decision-making powers to principals, dismantle much of the schools bureaucracy, and partially tie tenure review for teachers to test scores sets the stage for a fight with unions, advocates, and parents over how the new system will look.

In his annual State of the City speech to the City Council, Mr. Bloomberg also announced a new school funding formula that critics in the past have called a “backdoor voucher system,” which he said would balance differences in per-pupil funding among schools.

The cornerstone of the announcement, however, was a shift to school-based accountability, which could unleash school principals from much of the current bureaucratic oversight and supervision.

“We’ve always known that great principals make great schools. But until now, we haven’t always given them the full authority they need in order to lead,” Mr. Bloomberg said. “The principals will be in charge of what’s best for their students, always.”

Experts, education advocates, and parents are responding to the announcement with caution, with some applauding the emphasis on school-based accountability.

“You’re not going to have a series of dopey dictators — good principals will involve their staff,” the president of the Center for Educational Innovation, Seymour Fliegel, said. “You’re empowering teachers and parents, and you’re encouraging ownership of the school.”

But many were frustrated about a lack of details, and said they may oppose the plan once they know more.

“There needs to be appropriate oversight and training, so principals aren’t running around willynilly,” the chair of the City Council education committee, Robert Jackson said.

“The latest education reform initiatives are neither clear nor confidence-inspiring,” the city’s public advocate, Betsy Gotbaum, said. “In the area of school reform, we seem to be going around in circles, obsessing over what an organization chart should look like, waffling back and forth between old and new.”

Others were also critical. The president of the teachers’ union, Randi Weingarten responded to Mr. Bloomberg’s suggestion of a more rigorous process for tenuring teachers by saying that the process in the union contract recently approved by Mr. Bloomberg is already sufficiently demanding. The schools chancellor, Joel Klein, said the overhaul of the system six years into the mayor’s administration was necessary to create the conditions for improved academics and student achievement. Mr. Klein promised more information about the exact nature of the structural changes in the coming month.

“You will see years of discussion on the academic standards and core curricula,” Mr. Klein said. “But what you won’t see is reorganization of systems to go through the kind of transformation that will create, I think, the opportunity move the system to an entirely different level.”

In his speech, Mr. Bloomberg said the schools would return to the old bureaucratic structure of 32 districts, which his administration had originally tried to eliminate and replace with a structure of 10 regions two years ago. He was blocked by a lawsuit, however, and since then, the regional and district offices have existed alongside each other, although many community district superintendents until now had spent much of their time in regional offices.

Now, the 10 regions will be dissolved and replaced with three new types of bureaucratic formations. By next year, principals will have to choose which type of formation they would like to join. They can opt to become an empowerment school, the least restrictive of the three, which gives principals nearly complete control over budgets, programming and curriculum. They can become a partner with an external support organization such as a university or a non-profit. Or they can work with an “Internal Learning Support Organization,” the most restrictive of the three options, which would be a system resembling four “super regions.”

Most principals would largely operate without the supervisory structures currently in place, although community district superintendents would retain their ability to hire and fire principals and a new accountability initiative would provide a grading scale of A to F for schools that would determine the fate of principals.

The president-elect of the city principals’ union, Ernest Logan, said principals would welcome the increased power, but he said he worried they wouldn’t get enough support under the new system.

“We are particularly concerned about how these plans will impact education administrators and supervisors, whose expertise plays a crucial role in supporting schools, school leaders and most importantly, students,” Mr. Logan said. Beyond giving principals more control over their budgets, Mr. Bloomberg said his proposal to balance per-pupil expenditures would make the flow of money more transparent to principals and the public.

The new school funding formula, which has been called “weighted student funding,” would assign the same amount of money to each individual student. The amount would increase for low-income students, students who speak limited English and special education students. The money would then follow students as they moved between schools, causing some critics to compare it to vouchers.

A vice president of the Thomas B. Fordham Foundation, Eric Osberg, a proponent of student weighted funding, applauded the change from the current system where schools receive money from up to 90 different funding streams.

“It’s bold and it’s what the city should be doing,” he said. “Weighted student funding is about much more than choice. It’s about fairly funding students.”

The lawyer for the Campaign for Fiscal Equity, Michael Rebell, who has criticized weighted student funding in the past by saying it undermines efforts to increase overall funding for needy school districts, urged caution. He said the city should not just focus on equalizing per-pupil spending but also ensure that each school has funding for basic resources, such as science labs and libraries.

“I’m not sure weighted student funding is the best way to make sure the needs are getting met,” Mr. Rebell said. “We need to guarantee that every school has some of the basic building blocks.”

The director of the Campaign for Fiscal Equity, Geri Palast, also reacted cautiously.

“We need to know more,” she said. “God will be in the details.”