U.S. President Donald Trump on Saturday evening backed away from prohibiting travel in and out of the New York area to limit the spread of the coronavirus from its U.S. epicenter – an idea he had floated hours earlier – as the number of deaths crossed 2,000 nationwide.

With the death count doubling from three days ago, Trump initially said he might impose a quarantine on New York and parts of New Jersey and Connecticut to protect other states that have yet to bear the brunt of the outbreak. 

"They're having problems down in Florida. A lot of New Yorkers are going down. We don't want that," Trump told reporters.

However on Saturday evening he changed course, calling for a "strong Travel Advisory" instead.  

"I have asked the @CDCgov to issue a strong Travel Advisory, to be administered by the Governors, in consultation with the Federal Government," he tweeted. "A quarantine will not be necessary."

New York Governor Andrew Cuomo earlier said he had no details on a possible quarantine order.

"I don't even know what that means. I don't know how that would be legally enforceable, and from a medical point of view I don't know what you would be accomplishing," Cuomo told reporters. "I don't even like the sound of it."

In an interview with CNN's Ana Cabrera on Saturday evening, Cuomo likened the tactic to a "federal declaration of war." 

"It would be chaos and mayhem," he said. "It's totally opposite everything he's been saying. I don't think it is plausible. I don't think it is legal."

More than 52,000 of the country's cases are in New York state alone with nearly 6,500 people currently hospitalized. New York Mayor Bill de Blasio has said the city is trying to give health workers "relief" by bringing in reinforcements.

Some states have already imposed limits. New Yorkers arriving in Florida and Rhode Island face orders to self-isolate if they intend to stay, and the governors of Pennsylvania and West Virginia have asked visiting New Yorkers to voluntarily self-quarantine.

Read more:

New York completes first temporary hospital for coronavirus

Trump downplays coronavirus threat as U.S. records most infections in world

The United States now has roughly 120,000 confirmed cases, the highest figure in the world.

Trump has also been reluctant to invoke emergency powers to order U.S. companies to produce much-needed medical supplies, despite the pleas of governors and hospital workers, but has now ordered General Motors to make ventilators under the Defense Production Act. 

"General Motors MUST immediately open their stupidly abandoned Lordstown plant in Ohio, or some other plant," he tweeted, "and START MAKING VENTILATORS, NOW!!!!!!  FORD, GET GOING ON VENTILATORS, FAST!!!!!!"

He also appeared to soften his previous comments calling for the U.S. economy to be reopened by mid-April. "We'll see what happens," he said.