The city and the principals union have entered a mediation process after failing to agree on the terms of a new contract, union officials said Friday.

The move was made after the Council of Supervisors and Administrators and the city remained at odds over back pay for 2,000 members who had been promoted from teachers to administrators since 2009. Mediation is non-binding, but the step signals continued trouble with the negotiations, which began last spring.

“We were not making progress and agreed we should have someone come in and resolve our issues,” CSA spokeswoman Anne Silverstein said Friday.

The Department of Education declined to comment on the matter Friday.

Mayor Bill de Blasio and the United Federation of Teachers finalized a new teachers’ contract in May. The settlement with UFT ended a five-year period where teachers worked without contract. As part of the deal, teachers received retroactive pay that reached back to 2009.

But teachers were only eligible for those payments if they had been “continuously” employed as classroom teachers since 2009. Teachers who had since moved into management roles, and thus out of the UFT, were not eligible.

CSA officials said former teachers who became principals early in that window could lose as much $50,000 in back pay they would have earned if they remained in the classroom.

The provision has upset some principals, who have begun writing letters to the mayor’s office.

“The city should not penalize [principals] for taking on more responsibility,” P.S. 36 Principal Brandon Muccino wrote in a letter reprinted in CSA’s monthly newsletter.

Also included in the new UFT contract was a new 80-minute weekly block of professional development for teachers, which principals and supervisors must attend. The CSA filed a grievance with the Department of Education in mid-September over the addition of professional development time, which the union characterized in a recent newsletter as a “unilateral decision to increase the workday” for administrators.

Still, principals have expressed broad satisfaction with the city’s leadership. Schools Chancellor Carmen Fariña, who has instituted a new seven-year experience requirement for principals and often talks about the importance of principal leadership, recently earned a 91 percent approval rating from school leaders.

CSA and the city held the first mediation session on Oct. 30, and a second is scheduled for next week. If mediation fails to yield a settlement, the two sides could appear before a fact-finder assigned by the state to hear arguments from both parties and render another non-binding recommendation for resolving the dispute.

Correction: An earlier version of the story incorrectly stated the name of the CSA spokeswoman.