Writing for the majority, Justice Neil Gorsuch said the district’s new policy “greatly diminish[ed]” the court’s need to review the parent coalition’s case.

“The difficulty, as I see it, is that Boston has replaced the challenged admissions policy,” Gorsuch said in his response to the parents’ petition. “The parents and students do not challenge Boston’s new policy, nor do they suggest that the city is simply biding its time, intent on reviving the old policy.”

Justices Samuel Alito and Clarence Thomas dissented.

BPS’s temporary policy resulted in a significant decrease in the number of white incoming seventh graders who received admissions offers, and a small increase in admissions for Asian American applicants. The number of Black and Latino students admitted to the exam schools rose substantially.

The parent coalition sued BPS in 2021 on behalf of 14 white and Asian applicants. The parents sought to ban BPS from using criteria, such as ZIP codes and socioeconomic factors, as proxies for race in order to admit more Black and Latino students to exam schools at the expense of white and Asian applicants.

The coalition also sought to have five students who were rejected under the temporary plan admitted, arguing they would have been accepted under the old policy.

Chris Kieser, senior attorney at Pacific Legal Foundation, which represented the parent coalition, said in a statement the district’s use of students’ ZIP codes to allocate exam school seats violated the Constitution’s promise of equal protection under the law.

“Every student should have an equal opportunity to succeed based on their merit, not where they live or the color of their skin,” Kieser said. “Regardless of today’s disappointment, the government’s use of skin color or ethnicity to choose who can attend public schools is a critical constitutional question that must be settled.”

In his dissent from the high court’s denial, Alito said the district’s temporary policy was “racial balancing by another name” and “undoubtedly unconstitutional.”

Spokespeople for BPS did not return requests for comment.

The temporary policy was previously upheld by the federal district court in Boston and the First Circuit Court of Appeals. Oren Sellstrom, litigation director of Lawyers for Civil Rights, which represented two families who intervened in the lawsuit in support of the plan, said the court’s decision shows school districts should take steps to ensure that educational opportunities are available to all students equally.

“Our schools are stronger when classrooms are diverse and students from a wide range of backgrounds can learn from each other,” he said in a statement.

The justices earlier this year declined to hear a similar case brought by a group of Asian American parents who argued the race-neutral admissions criteria to the Thomas Jefferson High School for Science & Technology in Virginia were designed to increase enrollment of Black and Latino students. The policy set aside seats for a portion of students from every middle school.

Last year, the court struck down race-based affirmative action admission policies at Harvard University and the University of North Carolina.

Iván Espinoza-Madrigal, executive director of Lawyers for Civil Rights, said in a statement the Supreme Court’s action sends a clear message that there is “no appetite for extending the affirmative action decision beyond its narrow scope in college admissions.”

Deanna Pan can be reached at deanna.pan@globe.com. Follow her @DDpan.