Mr Trump told reporters at the White House that it would be for a “short period of time, if we do it at all”.
He said he had spoken to Florida governor Ron DeSantis and New York governor Andrew Cuomo about the idea. New York is currently the country’s epicentre of the coronavirus pandemic.
But Mr Cuomo said he did not talk about any quarantine with Mr Trump.
“I don’t even know what that means,” Mr Cuomo said during a briefing in New York.
“I don’t know how that could be legally enforceable, and from a medical point of view, I don’t know what you would be accomplishing. I don’t like the sound of it.”
It is not clear whether the federal government has the power to impose such restrictions on states.
Under the country’s constitutional system, states have the power and responsibility for maintaining public order and safety.
The federal government is empowered under the law to take measures to prevent the spread of communicable diseases between states, but it is not clear that means Mr Trump can order state residents to stay put.
Mr Trump made the comments on his way to Norfolk, Virginia, to see off a US Navy medical ship en route to New York to help with the pandemic response there.
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