The CDC said this advisory does not apply to employees of critical infrastructure industries, including but not limited to trucking, public health professionals, financial services, and food supply. These employees of critical infrastructure, as defined by the United States Department of Homeland Security and have a special responsibility to maintain normal work schedules.
The move comes, he said on Twitter, after consulting with the governors of the three states, who will administer the plan "in consultation with the Federal Government." The CDC said that the governors of the states would have "full discretion" on how to implement the advisory.
Trump said in his tweet that a quarantine would "not be necessary."
"I don't even know what that means. I don't know how that could be legally enforceable," the Democratic governor said during in a news conference in Albany. "And from a medical point view, I don't know what you would be accomplishing."
"But I can tell you, I don't even like the sound of it," he added.
"It would be chaos and mayhem," Cuomo said. "It's totally opposite everything he's been saying. I don't think it is plausible. I don't think it is legal."
Trump, however, earlier said that possible quarantine would be "enforceable" and "restrict travel" from those parts of the tri-state area. He also said any quarantine wouldn't affect truckers from outside the New York area.
"Restrict travel, because they're having problems down in Florida, a lot of New Yorkers going down. We don't want that," he said.
Florida Gov. Ron DeSantis said during a call with Trump, the President mentioned the possibility of a quarantine "around the New York City area."
"There's a lot of logistics involved and I think the President is well suited to figure that out," DeSantis said during a Saturday briefing. "Whatever works I think we need to do."
DeSantis said it's not fair to Floridians "to just be airdropping in people from the hot zones, bringing infections with them." He added that New York officials were working hard and doing a great job but people are "dispersing from there."
Sen. Richard Blumenthal, a Democrat from Connecticut, responded to Trump's tweet with one of his own, saying that the possible quarantine measures are "unclear" and could cause "confusion."
As he departed from Joint Base Andrews, Trump said he would speak to Cuomo later about the possible quarantine. And describing the quarantine as something that would be "for a short period of time, if we do it at all," the President also said that he would not close the New York City subway.
The National Guard helped coordinate delivering meals to those in quarantine and a drive-thru coronavirus testing site was opened.
As of Saturday morning, New York had at least 728 reported deaths due to coronavirus and at least 52,318 reported cases -- making it the state with the most in the nation, according to CNN Health's tally.
The legislation, passed in the 1950s on the cusp of the Korean War, provides the President with a broad set of federal powers to require businesses to "prioritize and accept government contracts" as well as "provide economic incentives" to ensure the US has the stockpiles it needs to handle an impending medical crisis.
The President on Saturday did not identify which companies or supplies he would use the order to produce, but he did suggest he was facing push back from companies he called "little problem children."
"We're look(ing) at two companies that have not lived up to what they said. I would say they're in the 1% group, okay? And all of a sudden they heard we're going to use it and they're rolling out the red carpet," he said.
Trump, in his remarks Saturday afternoon in front of the USNS Comfort before it departed for New York, expressed his gratitude to "the dedicated service members who will soon be on the front lines of this fight."
"This great ship behind me is a 70,000-ton message of hope and solidarity to the incredible people of New York," he said.
The Navy hospital ship will not treat patients with coronavirus, but rather provide surge capacity for those with other urgent care needs.
The ship is scheduled to arrive in New York on Monday and begin treating patients on Tuesday, Trump said.
Each ship contains 12 fully equipped operating rooms, 1,000 hospital beds, radiology services, a medical lab, pharmacy, optometry lab, a CAT-scan and two oxygen producing plants, according to the Navy.
This story has been updated to add the CDC's travel advisory.
CNN's Nicky Robertson, Christina Maxouris, Sheena Jones, Alisha Ebrahimji and Wes Bruer contributed to this report.