WASHINGTON — President Trump said Saturday night that he would not impose a quarantine on New York, New Jersey and Connecticut to prevent the spread of the coronavirus, but would instead issue a “strong” travel advisory for the region to be enacted by the governors of the three states.

Mr. Trump made the announcement on Twitter just hours after telling reporters that he was considering a quarantine of the area in an effort to limit the spread of the virus to Florida and other parts of the country, a move that would have been a drastic exercise of federal power to further restrict travel by millions of Americans.

Mr. Trump had offered no details about how his administration would enforce a ban on movements in and out of the three northeastern states, including the country’s most populous city, and the idea drew swift condemnation. Gov. Andrew M. Cuomo of New York called it a “declaration of war on states,” and Gov. Ned Lamont of Connecticut said it could cause confusion and panic.

The president appeared to heed those warnings, abruptly abandoning a proposal that he had floated with no notice on Saturday morning, once again subjecting the country — and, in particular, people in the northeast — to mixed messages about what his administration believed was necessary to defeat the dangerous pathogen.