“I think staffing capacity will be more of a problem than facilities,” said Cuomo, who added the state is reviewing how retired health care workers, the National Guard and medical students may be able to help.

In anticipation, some area hospitals have restricted travel for doctors in recent days in order to make them available for a patient influx.

Northwell Health and Mount Sinai Health System have asked physicians and other staff to stay close to home in case they’re needed.

“We are discouraging travel in general,” Terry Lynam, a spokesman for Northwell Health, said in an email. “All hands on deck. Our clinicians recognize this is a crisis situation and that now is not the time to go away.” Northwell is the region’s largest health system, with 23 hospitals and more than 5,500 beds in the city, Long Island and Westchester County.

The virus’s spread, designated a pandemic by the World Health Organization, could also strain stores of medical equipment on hand to aid patients with dangerous complications. New York has 7,241 ventilators statewide and another 1,750 stockpiled in warehouses in case of a public health emergency, according to a 2015 New York State Department of Health study. But more than 6,000 of those units were deployed in the care of elderly and chronically ill patients, meaning fewer than 3,000 would be available in a crisis.

Mitchell Katz, president of the city’s public hospital system, said there are about 5,000 ventilators at public and private hospitals across the city.

It’s likely that about 5% of those infected would actually need ventilators, Katz said. “People do get over this infection. Everybody won’t get sick at the same time.”

In remarks on Thursday, de Blasio estimated that the city’s next milestone would be 1,000 cases next week. He said at least 80% could be expected to be low-level cases that would not require hospitalization.

Even while preparing hospitals for a surge, officials made clear that containment and testing would continue to play an important role in the public response. Cuomo said he is banning gatherings of more than 500 people to address the virus's spread, with theaters and museums starting to turn away visitors.

The city is doubling down on disease detectives to trace the virus’s path, de Blasio said. New York city and state would have been able to better contain the disease, he said, if the federal government had allowed them to use their own tests. Tracing contacts is still useful in preventing clusters of the disease, he pointed out, as happened in the Westchester area north of the city.