After pouring an additional $4.5 billion into city schools over the last five years, Mayor Bloomberg is asking the Education Department to tighten its budget.

Overall spending in the schools will be higher than 2007, but projected increases are being scaled back, with the department outlining more than $500 million in cuts over the next two years.

On a list of about 20 line-item cuts outlined yesterday, principals are asked to shave $99 million in direct spending, an average of about $70,000 each; the Department of Education is to scale back a vaunted new program to test students regularly, moving to four tests a year from five, and, starting this June, an incentive program developed by the teachers union loses its central funding.

Principals who wish to keep the program, known as Lead Teacher, will have to pay for it with their own budgets, school officials said.

“As schools chancellor, I always want more money as my organizing principle. But as a responsible public official, when you see the downturns in the economy, the issues that the mayor will discuss, then you have to respond appropriately,” the schools chancellor, Joel Klein, said yesterday, speaking to reporters before Mr. Bloomberg delivered his proposal.

The mayor said the cuts are necessary in a tough economy.

They bring the total Department of Education budget to $7.1 billion this year from a projected $7.2 billion.

The department’s overall trajectory, however, remains up: In 2007, the city gave its schools $6.8 billion, and the 2009 budget, though down from a projection last June, is seen as rising from this year’s bottom line, to $7.2 billion.

Education advocates — still steaming from Governor Spitzer’s budget earlier this week, which gave the city schools smaller-than-anticipated increases — are likely to fight Mr. Bloomberg’s proposal, as well.

The president of the United Federation of Teachers, Randi Weingarten, said growing pressures on schools require that the city “protect core educational services.”

The executive director of the Center for Arts Education, Richard Kessler, said he is worried that a scenario from the 1970s fiscal crisis will play out again, with arts programs bearing “the lion’s share of the budget cuts.”

The vice chancellor of the state Board of Regents, Merryl Tisch, said she trusts that Mr. Bloomberg’s proposal is prudent. “Everyone knows how important education is to him,” she said. “So if the mayor is recommending these cuts, you could be sure that he’s not recommending them without having thought this through very carefully.”