Mr. Trump had come under intense criticism from Gov. Andrew M. Cuomo of New York, who assailed the idea as “a declaration of war on states.”

Mr. Cuomo, in an interview with CNN, expressed frustration and confusion over Mr. Trump’s vague suggestion that he was considering somehow sealing off New York, New Jersey and parts of Connecticut to slow the spread of the coronavirus, which has the New York City area as its epicenter.

The idea, Mr. Cuomo said, was at odds with Mr. Trump’s professed desire to restart the economy. “You would paralyze the financial sector,” the governor said.

But on Saturday night, Mr. Trump appeared to abandon the proposal, announcing on Twitter that, “A quarantine will not be necessary.”