The details of that quarantine seem to have evolved in both states since Friday.

“I didn’t reverse any decision,” Mr. Christie said from the Brevard Zoo in Melbourne, Fla., where he was campaigning for that state’s governor, Rick Scott, a fellow Republican. “She hadn’t had any symptoms for 24 hours. And she tested negative for Ebola. So there was no reason to keep her. The reason she was put into the hospital in the first place was because she was running a high fever and was symptomatic.”

After Ms. Hickox landed at Newark Liberty International Airport on Friday, a forehead scan showed she had a temperature of 101, which prompted concern because fever is a symptom of the Ebola virus. Ms. Hickox later said that the reading came because she was flushed and upset. A later reading taken with an oral thermometer recorded a normal temperature, 98.6.

“If people are symptomatic they go into the hospital,” Mr. Christie said. “If they live in New Jersey, they get quarantined at home. If they don’t, and they’re not symptomatic, then we set up quarantine for them out of state. But if they are symptomatic, they’re going to the hospital.”

On Sunday, Mr. Cuomo, a Democrat, relaxed New York’s mandatory quarantine, allowing New York resident health care workers to be at home and to be compensated for lost income.