Some of the region’s most famous landmarks, including the Statue of Liberty, Ellis Island and the Empire State Building, also shut down.

Mr. Lamont said on Monday night that the Danbury Hospital near the New York border was at capacity and that 200 nurses there could not report to work because they might have had contact with patients infected with the coronavirus.

The governor said there were not enough tests to determine whether the nurses had the virus.

“If I could test those nurses, I could potentially get them back into the game,” he said on MSNBC.

Earlier on Monday, Mr. Murphy had asked New Jersey residents to stay at home from 8 p.m. until 5 a.m. every day for now, a day after suggesting that he was considering a mandatory curfew.

“We are strongly asking, pleading with folks, to stay home,” Mr. Murphy said on Monday night. Asked how long the recommendation would be in effect, he said: “It certainly is at least weeks, and it may be many months.”

Like Gov. Cuomo, Mr. Murphy has activated the National Guard, whose members may be asked to work at testing sites, prepare hospitals for coronavirus patients, control traffic and deliver food to students who can no longer obtain their meals at school.