A judge denied a request for a temporary restraining order that the city was seeking to move ahead with a plan to close 24 city schools.
The city's teachers union has objected to the plan, which would have forced all faculty and administrators from those schools to reapply for their jobs.
An arbitrator earlier ruled in favor of the union.
City officials said the arbitrator exceeded his authority but the judge and a lawyer for the union said otherwise.
"It's a very common thing for the arbitrator to look at a contract and say that what one party did or another party did violated the contract," said Adam Ross, the general counsel for the United Federation of Teachers. "That's not exceeding the arbitrator's authority. That is exactly the reason why we have arbitrators. What the Department of Education doesn't like is that they want to be able to do whatever they want to do and not follow the contract."
The New York City Law Department said it is pleased the judge made it clear she wants to consider the case fully and is confident she will eventually conclude the arbitrator was wrong.
Both sides are due back in court on July 24.
See which public schools are facing overhauls.