“We are and have been reviewing this issue, and will continue to refine the state’s essential business guidance as the public health concerns dictate,” Jack Sterne, a spokesman for the governor, said. “All construction sites must enforce social distancing.”

“If a site cannot guarantee the health and safety of their ​workers, it must close,” he added.

Mayor Bill de Blasio, whose office is working with the state on possibly stopping some construction, said some of the work, like infrastructure and low-cost housing, remained vital.

“Luxury condos are not the priority in this city, but there’s a lot of other things being worked on that are important,” the mayor told reporters at a news conference on Sunday.

In recent weeks, Mr. Gibbs said, almost everyone he has worked with in upstate New York, including himself, have been sick with a cough, a runny nose or body aches. He said he was not aware of anyone who had been tested.

“They should really shut down these projects for two months,” he said. “I’d just hate to see more people die and get sick.”

A 37-year-old electrician working at an apartment building in Manhattan’s Financial District said that he asked the foreman at his construction site on Friday about whether their tools would be sanitized at the end of each day.

“He got offended and laughed at me,” said the electrician, who spoke on the condition of anonymity to share his story. He added that he has been carrying around a bar of soap he recently bought at CVS to wash his hands at work.