Civil rights leaders, clergy, parents, and educators issued a four-point action plan Wednesday to address concerns about racial inequalities at Boston Latin School and across the school system.

The organizers, in a news conference outside School Department headquarters in Roxbury, called for an overhaul of the admission policy for exam schools, which currently rely only on GPAs and scores from an entrance test for private schools. They did not propose specific changes.

They also urged Mayor Martin J. Walsh to include black educators, parents, and activists on a search committee for a new Boston Latin School headmaster and for the school system to implement a nearly decade-old policy to close achievement gaps that largely has sat idle.

Finally, they said everyone needs to work together to change what they called the climate of racial injustice that students, teachers, and others face daily.

“It is time for our city, our flagship public school, and our district to move forward in the best interest of all students,’’ said Jacqueline Rivers of the Ella J. Baker House, reading from prepared remarks as rain fell. “The city must ensure we don’t repeat the mistakes of the past.’’

The groups voiced their concerns one day after Superintendent Tommy Chang announced that former longtime Latin School headmaster Michael Contompasis would return as interim headmaster to help stabilize a school rocked earlier this year by allegations of racial discrimination.

Contompasis is part of a new leadership team that Chang is installing to replace outgoing headmaster Lynne Mooney Teta and a top assistant headmaster, who both resigned last week amid a federal probe into the school’s handling of racial incidents.

The School Department also launched its own investigations, which found that administrators acted insufficiently in six cases involving allegations of racial or ethnic bias out of more than 100 that were examined.

Responding to the organizers’ plan on Wednesday, the School Department addressed each point. It said a preexisting policy dictates the composition of the headmaster search committee, that it is in the process of updating and eventually implementing the achievement gap policy, that a working group is reviewing the exam school admission policy with an eye toward making changes that would increase student diversity, and that it is already taking steps to improve school climate across the system.

Concerns about racial discrimination came to light in January when two Boston Latin students, Meggie Noel and Kylie Webster-Cazeau, posted a YouTube video describing racial harassment and isolation at the nation’s oldest school, where 20 percent of the 2,400 students are black or Latino. Civil rights leaders subsequently filed a complaint with the US Attorney’s Office in Boston and had been calling for Teta’s ouster.

“The way forward is for us to acknowledge what has happened,’’ said Rahsaan Hall, director of the Racial Justice Program at the ACLU Massachusetts. “The way forward hopefully will begin as we learn what these investigations reveal and that these incidents students have raised, families have raised, and alumni have raised should not be dismissed out of hand and should not be given short shrift.’’

Hall was responding to comments made by some Teta supporters who believed the seriousness of the mishandled cases as well as the extent of racial discrimination at Latin School were overblown.

Wednesday’s press conference also included representatives from the Boston NAACP, Black Educators’ Alliance of Massachusetts, Massachusetts Advocates for Children, the Lawyers’ Committee for Civil Rights and Economic Justice, Urban League of Eastern Massachusetts, Azusa Christian Community, and Rev. Miniard Culpepper of Pleasant Hill Baptist Church.

James Vaznis can be reached at jvaznis@globe.com. Follow him on Twitter @globevaznis.