As many as 91 crew of an Italian cruise ship docked in Japan's southwestern port of Nagasaki are infected with coronavirus, officials said on Friday, as questions persist over how and when they will return to their home countries.

Authorities are racing to complete tests on about 290 of the 623 crew after one of them was found infected this week. The high rate of infections has fanned concern about the potential strain on medical services if patients' conditions worsen.

Those who have tested negative will be repatriated, Health Minister Katsunobu Kato said on Friday, according to Kyodo news agency, a decision welcomed by officials in Nagasaki prefecture.

"We're eager to get this done as soon as possible," a Nagasaki official told a live-streamed news conference, adding that it was not yet clear how repatriation would be completed, but authorities were in touch with the central government.

The vessel, the Costa Atlantica, was taken into a shipyard in Nagasaki in late February by Mitsubishi Heavy Industries after the pandemic scuttled plans for scheduled repairs in China.

The infections come two months after more than 700 passengers and crew of the Diamond Princess cruise ship docked in Yokohama port were found to be infected, although only crew were affected in this week's episode.

Just one of the Nagasaki ship's patients has been taken to hospital with severe symptoms, a local official said, while those with slight, or no, symptoms stay aboard.

The ship has been in quarantine, and Nagasaki authorities have asked that all crew stay aboard unless they require hospital visits.