Coronavirus Live Updates: U.S. Cases Near Record Level as Virus Surges in South and West

Nine states will be included, Mr. Cuomo said, when the restrictions take effect at midnight: Alabama, Arizona, Arkansas, Florida, North Carolina, South Carolina, Texas, Utah and Washington State.

Travelers to New Jersey and Connecticut would also be told to quarantine; their governors appeared with Mr. Cuomo to announce a tristate “joint travel advisory.” Mr. Cuomo said that enforcement would be up to each of the three states. Officials from New Jersey and Connecticut said there was no enforcement mechanism at the moment in their states.

In New York, those violating the quarantine order could be “subject to a judicial order and mandatory quarantine,” he said, and fines of up to $10,000. Mr. Cuomo also said that officials would not be stopping people at state borders to forbid them to enter, but that travelers were being asked to comply once they arrived.

A spokesman for Mr. Cuomo said that if a New Yorker believes that a recent arrival — or a returning neighbor — has not been abiding by the quarantine, then that person should start by reporting the possible violation to the local health department. Elsewhere in the U.S. where there are similar quarantines for travelers, there has not been widespread enforcement.

“You could argue that even law is the honor system until you get caught,” Mr. Cuomo said. “You can violate the quarantine until you get caught,” he added, then “you’re in mandatory quarantine and fined thousands of dollars.”

The goal, the governors said, was to maintain the hard-fought gains made in the region at great economic and human cost. For months, New York City particularly, as well as the state, had been a global center of the pandemic. Hospitals filled to near capacity. Hundreds died each day, reaching a peak in mid-April.

Many New Yorkers with the means to do so had fled, often to out-of-state locales. By late March, Florida began requiring travelers from the New York area to quarantine. Other states sought to restrict visitors. Researchers later found that by March, New York City had been seeding outbreaks around the country. But on Wednesday, Mr. Cuomo said there were only an additional 17 deaths statewide.