“The logic and the basis for the quarantine is that if people do not have a fever or show signs of sickness after 14 days, that they don’t have the virus,” Mr. Montgomery, the passenger, said. “But the problem is, on this petri dish of a ship, is that three days prior to the 19th, we may have an interaction with somebody in the hallway or on the deck” who is infected.

On Wednesday, he said, when the couple went out for a prescribed fresh air break, another passenger was coughing in the hallway as they returned to their cabin.

“So this whole thing is based on a false logic,” he said.

In a briefing earlier this week, Masami Sakoi, a health ministry official, said it was possible that people exposed to infected passengers would have to effectively reset the clocks on their quarantine periods.

Ms. Montgomery suggested that the governments of the countries with passengers or crew members on the Diamond Princess should offer to house people in quarantine facilities on land.

“If the U.S. embassy took the Americans off and took us away from here and quarantined and tested us and they did that with every nationality, I think that would be more effective,” she said.

Even so, finding space where such a large number of people could be safely isolated and given proper medical care could be a challenge, especially as Japan is now seeing fresh cases elsewhere. On Thursday, the health ministry announced three new cases, involving a taxi driver and a doctor, in addition to the death from the coronavirus.