“We rely on our contracts to do this work,” Mr. Apple said in a statement, “and the fact is that tens of millions in city funding is not available to us, limiting our ability to provide these critical services.”

Providers, particularly nonprofits running shelters, said they were reluctant to expand services or add beds, as needed by the city, because of the nonpayment.

Image Scott M. Stringer, the comptroller. Credit... Kevin Hagen for The New York Times

Anthony E. Shorris, the first deputy mayor, and Gilbert Taylor, the commissioner of homeless services, said they were indebted to the nonprofits for continuing to work with the city. But Mr. Shorris said that good will was being tested by the actions of the comptroller’s office. He said that the administration had tried to provide Mr. Stringer with the paperwork that he requested, but that the comptroller was overstepping his authority.

“When this comptroller or any comptroller uses any paperwork processes to slow down the registration of contracts, this mayor, like other mayors before him, will do what it takes to make sure vendors get paid,” Mr. Shorris said.

“To say they’re unhappy is an understatement, and we have to remedy this,” he added. “If we can’t ultimately satisfy the paperwork demands being made, we’ll just have to deem them registered and get them paid.”

Mr. Stringer said he was not impeding services to the homeless; he was just trying to ensure that facilities are safe. Though more than 50 contracts have not been registered, his office has approved 176 contracts to shelter providers in the past 20 months. He pointed to his cooperation in other ways, like approving three emergency requests in August for about $57 million to provide 1,421 beds for single adults and another 780 units for families with children. That emergency process bypasses monthslong procedures to free up money to negotiate contracts.