Under political pressure, a task force Tuesday changed its recommendations on a permanent admissions process for Boston's exam schools in a way one of its leaders says will limit increases in their racial-ethnic diversity.

The task force will recommend 20 percent of the invitations to each of the city’s three exam school be allocated to students by rank academic order city-wide, a shift from the policy the group had been hammering out over the last five months. Just a day earlier, the panel had reached a consensus that all invitations at each exam school be allocated to students within tiers related to census tracts and socioeconomic status.

“The data is very clear about who and what the 20 percent represents,” said co-chair Tanisha Sullivan, who is also president of the Boston NAACP.

Sullivan said she didn’t want to make a concession, noting that the 20 percent of invitations benefit white students from more prosperous neighborhoods who have acess to greater resources to prepare to win admission. Black and Latino students have been underrepresented at Boston Latin School, Boston Latin Academy and John D. O'Bryant School of Mathematics and Science.

“I am a student of the civil rights movement, and so what I know to be true is that this is not new,” she told the task force. “We cannot be deterred. I want to be clear about this 20 percent conversation. It is political. As I look at the data it is clear about who this benefits … and there are those who are adamant it must exist.”

Neither Sullivan nor the other co-chair, Michael Contompasis, disclosed the exact source of the political pressure, but the Boston City Council will vote this week on the $1.3 billion schools budget and could reject it if a majority objects to the admissions plan.

Contompasis offered a way to lessen the impact of the last minute political demands on increasing diversity. He recommended giving students in public housing or foster care or who are homeless a better chance at admission by adding five points to their composite entrance score, a combination of their GPA and entrance exam score.

A student's GPA will be weighted at 70 percent, and the exam score at 30 percent. In the past, the two factors carried equal weight. Students attending a high poverty school where more than half of students are economically disadvantaged would receive 10 additional points to their score.

Contompasis, a former headmaster of Boston Latin School, noted the political sacrifice Sullivan made and acknowledged members have put in 60 hours of work since February to craft their recommendations.

But he also warned the members that if they did not agree to the change, “there may well be an impact on the district that none of us want to see."

The remaining 80 percent of exam school invitations would be allocated to students within tiers under the latest task force recommendations, with the lowest socioeconomic tiers receiving offers first.

Boston’s exam schools have not changed their admissions policies in two decades and temporary changes to the policies have already led to a fierce legal battle. Earlier this year, a group of white and Asian Boston parents sued the district for alleged discrimination saying the temporary changes in admissions to the exam schools were racially motivated and discriminatory.

But U.S. District Court Judge William G. Young ruled in April that the plan was "race neutral" and allowed grades and zip codes to be used to assign students for the upcoming year. The school department said a traditional entrance exam could not be administered this year because of the pandemic.

The 13-member task force had been charged with drafting a permanent plan that would expand diversity at the schools.

While several members said they would get behind the changes, four members said they disagreed or felt conflicted about the last-minute revisions.

Task force member Zena Lum, a parent of a student at Boston Latin Academy, expressed frustration. The task force’s charge was to create a more racially, geographically and economically diverse student body, and it had crafted a plan designed to accomplish those goals.

“We had a consensus, and it was taken away from us,” she said. “It has been taken away from us, not that it hasn’t been reached.”

Task force member Roseann Tung, a researcher, said the schools need more equity and justice, not 20 percent “set asides for the powerful.”

The panel ultimately agreed to present the recommendations to the school committee.

Sullivan said Superintendent Brenda Cassellius will present their recommendations to the school committee at its regularly scheduled meeting on Wednesday evening. The committee plans to vote on the recommendations in July. If approved, the changes would take effect in two years.

GBH News reporter Saraya Wintersmith contributed to this report.