The city Department of Education is rolling back part of an ambitious plan to expand its identification of gifted and talented children by giving all kindergartners a screening test.

Chancellor Joel Klein last year said he wanted to expand screening so that programs often dominated by well-connected and affluent white parents could include a more diverse group of students. The program was also supposed to improve kindergarten teaching by giving instructors an idea of the “baseline” ability with which every kindergartner is entering school.

At a City Council hearing yesterday, Mr. Klein said that, as a way to handle budget cuts handed down by Mayor Bloomberg, the department will not actually test every kindergartner next year.

A department spokesman, Andrew Jacob, said the move is also intended to show parents that there is no requirement their children be tested as kindergartners. They can opt out of the testing if they choose.

Had it been implemented, the extra testing would have cost about $1.5 million, Mr. Jacob said.

Changes to the screening process that were made this year would be preserved. Those changes — including holding tests at school buildings, during school hours, and substantially expanding outreach efforts to advertise the gifted and talented programs — have already almost tripled the number of students taking gifted and talented exams.

This year, almost 24,000 kindergarten and first-graders took the exams, compared to about 8,000 last year, school officials said.

Thus, Mr. Jacob said, most of Mr. Klein’s efforts to expand access to gifted programs has been preserved.

“I think that to characterize this as rolling back G&T access is objectively wrong,” Mr. Jacob said.

The decision was greeted as a victory by an anti-testing advocacy group based in the city, Time Out From Testing, which has described the policy as a concealed effort to “track” students beginning at a very young age. The group argues that tests of such young children’s abilities are inaccurate and potentially damaging.

“It’s about the tracking of children, and to think that they would do it for a 4-year-old or a 5-year old, it’s criminal,” the group’s co-chairwoman, Jane Hirschmann, said yesterday. “We see this as a huge victory.”

The gifted-program change was a rare point of certainty at yesterday’s budget hearing, where City Council members grilled Mr. Klein on his plans for incorporating recommended cuts into next year’s education budget.

Although Mr. Bloomberg proposed cutting the Department of Education’s budget along with those of most other city agencies, it is becoming increasingly clear that the council will not go along with that proposal without some revisions.

Nearly all members of the council and Speaker Christine Quinn are vowing to add more funds to the education budget in particular as a way to insulate classrooms from Mr. Bloomberg’s proposed cuts. Ms. Quinn said that hammering out ways to do this would be her goal in meetings this week between her staff and people at the Department of Education.

She said she plans to target “managerial contracts” the department holds with outside groups. Shaving from other agencies could be another way to recover funds, she said. One proposal she listed would cut an extra $70 million from the human resources administration.

Before a deal can be reached, one mystery must be solved: precisely how much money it takes to prevent cuts from affecting classrooms.

The group led by the teachers union and the Campaign for Fiscal Equity puts the figure the highest of all, at $450 million.

Mr. Klein is saying that number is about $400 million, but could drop substantially if the state agrees to loosen certain restrictions — an idea that two key players, Governor Paterson and the Assembly speaker, Sheldon Silver, are indicating they would block.

Finally, Ms. Quinn said yesterday that her staff’s estimate of what it would take to insulate schools from budget cuts is lower, around $200 million.

At the hearing, council members took turns grilling Mr. Klein on the numerical discrepancies.

“The fact that there are so many numbers floating around is troubling,” Ms. Quinn said.

Other members were more extreme.

Council Member John Liu of Queens said the confusion damaged the Bloomberg administration’s credibility. “You’re not being forthright with people here,” he said.

Council Member Oliver Koppel of the Bronx suggested that Mr. Klein was lying about the budget figures.

“To tell you the truth, I don’t believe you,” he said.

“You should hire a new accountant,” he added, interrupting an explanation by Mr. Klein.

Saying he spoke for about a handful of lawmakers, Council Member Peter Vallone Jr. of Queens rose to Mr. Klein’s defense on the budget question, saying he did not share the rest of the council’s criticism of Mr. Klein for not standing up to Mr. Bloomberg.

“We don’t expect you to be cheerleader-in-chief,” Mr. Vallone said.