Ceding ground to the city teachers’ union, Mayor Michael R. Bloomberg announced changes yesterday to his plan for a new school budgeting system. The changes mean that it will be harder and take longer for the mayor to redistribute senior teachers, who tend to cluster in middle-class neighborhoods, more evenly across the school system.

The mayor also reached accords yesterday with an array of interest groups, which like the union have loudly opposed his latest plans to reorganize the school system. Among these, Mr. Bloomberg agreed to a demand by the New York Immigration Coalition for an increase in money allocated for children with limited English proficiency.

Mr. Bloomberg; Chancellor Joel I. Klein; the union president, Randi Weingarten; and many of the groups gathered at City Hall yesterday afternoon to announce the deals. The agreements with these groups, which included Acorn, New Yorkers for Smaller Class Size, and the Coalition for Educational Justice (Make the Road by Walking is a member), bought the mayor some measure of political peace after weeks of complaints about his handling of the schools. The groups agreed to pull back plans for a big protest early next month.

"Over the last few days, we have realized that we are a lot closer together on many of the issues surrounding school initiatives than some might have thought," Mr. Bloomberg said. "Now we are ready to move forward to achieve some of our common goals."

But experts on education financing warned that the mayor was at risk of undermining his effort to bring equity and transparency to the school budgeting system.

"There are political deals that you have to cut around some of these things," said Andrew J. Rotherham, co-director of Education Sector, a research group based in Washington. "At the same time it’s important that policy makers keep their eyes on these things, because where policy reforms go to die is when policy makers keep cutting these deals."

Earlier this year, Mr. Bloomberg called for ambitious changes to the school system. The revised budget system was just one aspect of it, intended to address inequities in financing and teaching quality between schools. He also said he would require teachers to undergo rigorous review to gain tenure.

But the plans drew an outcry from teachers, parents and political opponents. And yesterday’s deals were intended to tamp down the dissent.

The mayor agreed to consult with the union, the United Federation of Teachers, as he moves to tighten tenure requirements, giving the union input on one of the most sensitive topics to its members.

The deals also call for the city’s Education Department to establish committees to improve parent relations, to comply with a new state law requiring the city to reduce class sizes, and to provide oversight of the new budget process. In addition, the administration agreed to work with the City Council speaker, Christine C. Quinn, on improving middle schools. Ms. Quinn has formed a task force that is studying the issue.

Under the city’s current budgeting process, schools receive a set number of teachers and the city provides the money to cover their salaries. Schools with large numbers of high-paid veteran teachers, many of them with high-performing students, can maintain large payrolls.

The mayor’s new system would ultimately finance schools based strictly on numbers of students and their needs, with extra money provided for children from low-income families, for students needing English language instruction, for disabled students and for high-achieving students. And principals would have to meet payroll.

Previously, Mr. Bloomberg had announced plans to lessen the impact of the changes by paying the salaries of teachers so long as they remained in their current posts. Only when a teacher retired, resigned or transferred would the principal have to consider the cost of a replacement.

But yesterday, Mr. Bloomberg said he would go even further. "Schools will still receive the funds even after a teacher transfers or retires," he said.

The change means that when a veteran teacher paid nearly $100,000 a year retires, a principal can hire a similar teacher or hire a rookie for about $50,000 and use the remaining $50,000 for other expenses.

The mayor said no school’s budget would be cut as the plan took hold.

"As we stopped yelling at each other a lot publicly and started talking to each other, you saw there were more areas of agreement than disagreement," Ms. Weingarten said.

Still, amid the declarations of newfound collaboration there were signs of tension. Both the administration and its critics insisted that they had conceded little.

And not all of the mayor’s critics signed on. Noticeably absent were members of elected parent groups; the leader of one such group issued a blunt statement criticizing the deals.

"This agreement provides no relief for disenfranchised parents who were once again denied a seat at the table," said Tim Johnson, the chairman of the Chancellor’s Parent Advisory Council, a citywide group. "Not one elected parent leader stood with the mayor today. Our fight for full empowerment for public school parents continues."

Also absent were representatives of groups that had hoped to reach a deal to limit the growing number of standardized exams that city schoolchildren face each year.