The state’s labor relations board has heeded a teachers union request to appoint a mediator to broker a compromise on teacher evaluations at 33 struggling schools.

City officials say will contest the decision, which could undermine the Department of Education’s chief justification for pursuing a reform strategy at the schools that would require many teachers to be displaced.

The ruling by the Public Employees Relations Board is a response to a request for mediation filed by the United Federation of Teachers in January. That request came a day after Mayor Bloomberg said that he would circumvent a collective bargaining requirement at the schools, which had been receiving federal funds to help them improve.

Because the city and union had not been able to agree on new teacher evaluations at the schools by a Dec. 31 deadline, Bloomberg announced that the city would switch the schools from the “transformation” and “restart” reform processes, which require new evaluations, to “turnaround,” which does not. Chancellor Dennis Walcott argued at the time that the switch made PERB’s intervention moot because the board has authority only in collective bargaining matters, and turnaround does not require collective bargaining.

But the city has not formally asked the state for permission to assign the schools to turnaround or withdrawn its application, submitted last summer, for funding for transformation and restart. PERB’s director of conciliation, Richard Curreri, said those facts led him to conclude that the city is still bound by its 2011 agreement to negotiate new teacher evaluations at the 33 schools.

In a letter explaining his decision to Walcott and UFT President Michael Mulgrew, Curreri says he would appoint a mediator to help broker a compromise.

But the city won’t return to the bargaining table without a fight. “We strongly disagree with this decision and will take all appropriate legal action to have it reversed,” Matthew Mittenthal, a Department of Education spokesman, said in a statement.

The ruling carries high stakes for both parties. The union wants to avoid turnaround’s requirement that schools replace half of their teachers. The city, on the other hand, is committed to carrying out the turnaround plans, with or without federal funds, in part because Bloomberg believes that turnaround would be speedier than tougher evaluations at moving weak teachers out of the classroom.

A deal on evaluations at the 33 schools would remove the city’s chief justification for turnaround. And a deal would seem to be more in reach than in January, when the city and union were seemingly irreconcilably divided on how to handle appeals of teachers who receive low ratings under a new evaluation system. Since then, Gov. Andrew Cuomo pushed the city and union to agree on an appeals process, meaning that there is no longer an obvious obstacle to new evaluations and less disruptive overhaul strategies for the schools.

It would be very difficult for the city to execute new evaluations in the 33 schools this semester, a requirement for receiving the federal funds. Had a deal been reached in December, the schools would have issued assessments this semester to generate the 40 percent of teachers’ ratings that must be based on student performance. When the talks fell apart, so did that plan.

Curreri’s letter suggests that one way for the department to avoid resuming evaluation talks for the 33 schools would be to submit applications for turnaround at the schools. Mittenthal said again today the department planned to do so but did not set a timeline.

Originally, department officials had set an early-February deadline to submit the turnaround applications to the state, but it did not meet that deadline. Lately, officials have been indicating that they would wait until the planning process is farther underway at the schools before formally notifying the state of the plans.

Curreri’s letter, in which he says the decision required him to parse a “seemingly arcane issue,” is below.