In 2018, Latino and Black families in New Jersey filed a lawsuit that landed like a gut punch to the state’s progressive reputation. Public schools in New Jersey were alarmingly segregated, the plaintiffs argued, in violation of the state Constitution.

The case kicked around in the courts for years before a judge released a decision in October that made neither side happy. The next step might have been a march toward trial and years of legal wrangling that would have been likely to push the problem to New Jersey’s next governor.

But late last year the state’s attorney general, Matthew J. Platkin, opened the door to compromise. He suggested that the parties enlist a mediator and begin settlement talks, thrusting New Jersey into an inadvertent starring national role.

Cities in many states, including Connecticut, Minnesota and New York, are actively wrestling in courts and classrooms to improve racial integration within school districts, and, in some cases, broad regions. But no state has voluntarily sought a statewide remedy to segregation in the 70 years since the Brown v. Board of Education decision outlawed government sanctioned, racially separate schools.

The next mediation session is set for Friday, just as a new school year is beginning for New Jersey’s 1.4 million public school students.

The state’s negotiating team, led by the attorney general’s office and education department officials, has been in talks with the plaintiffs now for nearly 10 months. People with knowledge of the confidential discussions say they are nearing a pivotal moment and that success is far from certain.