YOKOHAMA, Japan — Japan announced a new plan Thursday to gradually test passengers on board the stricken Diamond Princess for the new coronavirus and allow some to disembark before the end of the quarantine period, as fears rise that the virus may still be circulating on board the cruise ship.

Health Minister Katsunobu Kato said Thursday that 44 more people on board have tested positive for the new coronavirus on the quarantined cruise liner, bringing to 218 the total found to have the virus, including 21 crew members.

On shore, Japan announced its first death from the coronavirus, a woman in her 80s in Kanagawa Prefecture, the same region outside Tokyo where the ship is docked, and three more cases of the virus, a taxi driver in Tokyo, a man in his 20s in Chiba near Tokyo, and a doctor in the east of the country.

That news will put further strain on Japan’s limited ability to test people for the virus and pose some tough questions on where to concentrate limited resources.

For now, though, there is a new focus on getting people off the Diamond Princess, after a sharp rise in the number of people found to have the virus that has fueled fears it could still somehow be spreading on board, possibly through the crew who prepare and deliver meals.

Amid mounting criticism, Japan’s government changed course on Thursday, announcing that it would begin a phased program of testing, where passengers who have no trace of the virus will gradually be allowed to disembark before the quarantine ends on Feb. 19, on a voluntary basis.

Kato said the program would begin with the most medically vulnerable people, the more than 200 people in their 80s on board, and those with health problems that put them at particular risk. Priority will also be given to people with indoor, windowless cabins, while gradually extending the age range of evacuees.

They will be taken to a quarantine facility with individual rooms and bathrooms, but no medical clinics on site, the U.S. Centers for Disease Control and Prevention wrote in a letter emailed to the American passengers on board.

“Please be aware this process will take time, and not everyone may be offered a chance to disembark before the end of the quarantine period,” CDC Deputy Director Anne Schuchat wrote. “We understand this is an incredibly stressful situation. We appreciate your understanding and patience as passengers are tested and their movements planned accordingly.”

Melanie Haering, 58 and her husband John, 63, from the city of Tooele in Utah, needed all of their reserves of patience when he came down with a high fever on Monday evening.

With his temperature shooting as high as 39.8 Celsius (103.6 Fahrenheit), they had to wait until Tuesday at 5 p.m. for doctors to arrive, and until Thursday morning for him to be taken to hospital and finally be tested for the virus.

Ironically, by then, the fever had subsided.

“Today, he felt fantastic, he had his appetite back,” she said. “This morning they called and he was in the shower and they said, ‘we’re coming to get you in about 20 minutes,’ and he was taken to the hospital. So he packed a bag — he really didn’t want to go because he felt so good.”

In two days, John Haering will find out if he has coronavirus. Melanie says she has asked to be tested herself but doesn’t know if and when that will happen — partly because she was communicating in English with doctors speaking Japanese.

Still, she is keeping a positive outlook about their trip, part of a six-month retirement journey that has already taken them to Singapore, Malaysia, Indonesia and Thailand.

“It really hasn’t been that bad,” she said. “If this is my trial in life, this is easy.”

So far, more than 30 percent of the 713 people who have been tested for the virus have been found to have been infected. That makes it statistically virtually certain that more people among the 2,666 passengers and 1,045 crew have the virus.

While the CDC and the World Health Organization have backed the Japanese government’s handling of what is an unprecedented health crisis, questions continue to be asked why Tokyo didn’t move more quickly to test people on board and get them off the ship.

“I personally believe that this [quarantine] is a fundamental violation of human rights, and it’s a very risky situation to be in,” said Lauren Sauer, director of Operations with the Johns Hopkins Office of Critical Event Preparedness and Response. “There are so many people on the ship who are potentially now exposed and their risk continues every minute they are on the ship.”

Hong Kong managed to test 1,800 crew members on board another cruise ship, the World Dream, in just a few days and allow everyone to disembark, but Japan has limited capacity to test for the virus and competing demands from around the country of 127 million people, officials say, with 32 confirmed cases of coronavirus already.

Last week, a government official said the country could test 1,000 people a day nationally. On Wednesday, Prime Minister Shinzo Abe spoke of administering 300 tests a day to boat passengers but said the government aimed to raise that number to 1,000 by the time the cruise ship’s quarantine is over, so people can be tested before being released.

But tests are not completely reliable, nor would they have been a panacea, experts said.

Outbreaks of norovirus, a highly contagious stomach bug, are fairly common on board cruise ships — the CDC’s Vessel Sanitation Program recorded eight last year among 10 virus outbreaks on cruise ships — and the usual practice is to clear everyone off the ship and then decontaminate it, said David Hamer, a professor at the Boston University School of Public Health and School of Medicine.

“Looking at the way a typical norovirus outbreak would be handled, they wouldn’t keep them on the ship they would get them off the ship … to make sure they are not at risk of ongoing exposure,” he said. “I think it’s really hard to prevent continued transmission in a context like that. It might have made more sense to act differently in the beginning.”

Passengers say the captain has repeatedly assured them that the air circulating in their cabins is fresh rather than recycled. But the risk of catching the virus on board still bothers many people, whether by talking to people in neighboring cabins across balconies, walking past them on occasional trips outside their cabins for exercise, or through the delivery of food and drink.

Spencer Fehrenbacher, a 29-year-old Fulbright scholar studying at Tianjin Foreign Studies University in China, says he was among the very first group of 273 people tested for the virus — because he had come down with a fever a few days before. An agonizing few days’ wait ensued, with passengers not told their test results unless it was bad news.

“The reality was that at any point we could get the ‘knock of doom’ on the door, and we’d have an hour to pack up and leave,” he said.

But the knock never came, and Fehrenbacher, whose family emigrated in 2016 from the United States to Vancouver, B.C., was eventually able to conclude the test was negative. Like the Haerings, he’s found ways to keep himself busy while remaining patient and staying positive.

Still, as the number of sick crew members has climbed, he’s decided not to take any chances.

“Starting yesterday, we decided that when we get silverware delivered, we take this plastic kettle and we fill it with water and we get the water nice and boiling, and then we stick our silverware in there for five plus minutes, to do everything we can to ensure that it’s sterile,” he said.

Fehrenbacher hopes he might get off the boat before Feb. 19, but doesn’t expect to be evacuated ahead of the many elderly people on board.

“I think it’s a little selfish to want to say, ‘okay, I need to be at the front of that line’ when in reality, you know, if I ended up contracting this, it’s going to be an unpleasant couple of weeks, but I have a lot better outlook than a lot of my fellow passengers here,” he said.

Berger reported from Washington and Kashiwagi from Tokyo.