On Friday, Mr. DeSantis extended his quarantine order to cover travelers from Louisiana as well, and authorized highway checkpoints in the Panhandle to intercept and warn them.

President Trump said on Saturday that concerns raised by states like Rhode Island and Florida about travelers from New York City had prompted him to consider imposing a federal quarantine of New York, New Jersey and part of Connecticut. He later backed off the idea.

Legal experts said that states were on shaky ground pulling people over just for their license plates. And Gov. Andrew M. Cuomo said on Saturday that Rhode Island’s action was “at the point of absurdity.”

“If they don’t roll back that policy, I’m going to sue Rhode Island, because that clearly is unconstitutional,” Governor Cuomo said on CNN, though he added that he didn’t think it would come to that. “We’ll work it out amicably, I’m sure,” he said.

Even so, Rhode Island’s measures were welcomed by many “year-rounders” who live in the state’s summer resort communities near the Connecticut border. They have been growing increasingly frustrated with an influx of New Yorkers fleeing the city to second homes and rental properties in the area, and possibly bringing the virus with them.

Local residents have been posting videos and photographs in local Facebook groups of cars with New York tags being pulled over.

John Austin witnessed a stop on Friday in Westerly, a town of about 23,000 in the corner of the state nearest to New York, when a trooper’s flashing lights followed a driver into the parking lot of Sandy’s Fine Food Emporium, where Mr. Austin is the store manager.