A passenger who left the Diamond Princess after completing the cruise ship's quarantine has tested positive for coronavirus.

The Japanese woman in her 60s is the first known case of infection among those released at the end of the ship's containment period, local officials say.

Tochigi prefecture's governor Tomikazu Fukuda said the woman tested negative for the virus on February 15, four days before she got off the ship with her husband, with neither showing any symptoms at the time.

A Japanese passenger from the cruise ship Diamond Princess who was given the all-clear after a quarantine period has since tested positive for coronavirus. (AP)

The couple took a train home, officials said on Saturday (local time).

Despite strong doubts raised from inside and outside the country, Japanese health ministry officials have insisted that any passengers who completed the 14-day quarantine, tested negative for the virus and showed no symptoms had nearly zero risk of becoming a virus patient.

"I would like to urge the government to take more thorough preventive measures," Mr Fukuda told a news conference.

Some experts and former passengers have criticised the quarantine, saying anti-infection measures were inadequate.

The US, Australia and other governments that evacuated their citizens from the ship are requiring them to undergo an additional two-week quarantine.

The Japanese woman in her 60s is the first known case of infection among those released at the end of the ship's containment period, local officials say. (AP)

Japan's health minister Katsunobu Kato said 23 passengers had been released from the Diamond Princess at the end of the quarantine without being tested for the virus due to procedural mistakes.

He said the 23 were tested before the quarantine began on February 5, but were allowed to leave the ship on Wednesday and Thursday without being tested again.

Three of them have since tested negative, and most of the others have agreed to be tested, he said.

Kato said officials have tracked all 23 passengers down and asked them to self-quarantine at home for 14 days.

"We deeply regret that there was an operational error," he said at a news conference.

"We will examine what went wrong so we will not repeat the same mistake."

Japan has confirmed more than 760 cases of the new virus, which first emerged in China, including at least 634 from the Diamond Princess, which docked and was quarantined in Yokohama, near Tokyo.