The governor told the hospitals to double capacity in expectation of a rising tide of sick people. The influx was already apparent at places like NewYork-Presbyterian, where officials said they’d seen more than 500 coronavirus patients by Sunday morning. The hospital instituted a variety of rules to control spread of the virus, including banning partners from pregnant women’s delivery rooms.

The state was also repurposing existing health care facilities including nursing homes to act as temporary hospitals, even as the Federal Emergency Management Agency and the U.S. Army Corps of Engineers made plans to turn the Javits Center into a temporary medical center.

All told, upward of 2,000 beds will be prepped inside the convention center, some manned by federal emergency personnel. The governor was still asking for more help with staffing and supplies, saying that the states were vying for the same emergency products, causing prices for basic items like protective masks to soar.

“This state cannot manage it, states all across the country can’t manage it,” said Mr. Cuomo, a third-term Democrat, adding, “I’m competing with California and Illinois and Florida, and that’s not the way it should be.”

He also asked President Trump to utilize the Defense Production Act, a Cold-War-era law which allows factories to be repurposed, mixing praise for the president with more direct appeals for assistance from federal authorities.

New York was not alone in tightening rules surrounding businesses and its citizens’ daily lives: there were similar strictures in California and Illinois, and in neighboring New Jersey, which reported nearly 2,000 cases as well, including 20 deaths.

There were also signs that emergency personnel were beginning to bear the brunt of the disease. New York City police officials said Sunday that the department had 98 confirmed cases, including 28 civilian employees.