Hundreds of teachers-turned-administrators could lose out on tens of thousands of dollars in retroactive pay due to teachers if the city has its way in contract negotiations, according to principals union officials.

City officials have insisted in negotiations that teachers who move into administrative positions any time during the life of the contract — from November 2009 until final payments are made in 2020 — are ineligible for their share of the roughly $3 billion in back pay and retroactive raises agreed upon in the new teachers contract, the principals union officials said.

“This is unjust for those of you who have earned those percentage increases and it also serves as a powerful disincentive for those teachers contemplating a promotion,” Ernest Logan, president of the Council of School Supervisors & Administrators, or CSA, said in an email Tuesday to principals union members. He called the city’s position on the matter “outrageous.”

About 2,000 CSA members have been promoted since 2009, and many more are expected to be in the coming years, according to the union, which is still negotiating a new contract for the principals, assistant principals, and other administrators it represents.

The city-teachers union deal, which was ratified last month, grants teachers back pay from the first two years when they worked without a contract, but says the money will be paid out in chunks from 2015 to 2020. For instance, a teacher who earned a top salary of $100,049 in 2009 is due to receive a total of $54,000 in retroactive pay disbursements by 2020. But if the teacher becomes a school leader before that time, she would forfeit whatever portion of the back pay she had yet to receive, the officials said.

“If it is truly retroactive pay, you’re being paid for work you already did,” said Joanna Cohen, an assistant principal at P.S. 2 in Chinatown who had expected to receive back pay for the years she worked as a teacher without getting raises. “Now you’re not being paid for what you worked.”

A similar issue arose in the city and teachers union negotiations, where it was decided that teachers who resign before the back pay is issued would not receive any of that money. Now, some of those teachers are suing the teachers union for that pay.

But in the case of the principals contract, the educators who stand to lose out on the retroactive money have not quit but instead were promoted to new roles by the Department of Education.

“Penalizing the very people the DOE has chosen to promote doesn’t seem to make that much sense,” said a union official familiar with the negotiations. The official said the back-pay dispute represents a major roadblock in the negotiations.

“Until this gets figured out,” the official said, “I have a hard time seeing how we’re really moving forward.”

Spokespeople for the mayor’s office and the education department did not immediately respond to a request for comment.