The ship docked at a Yokohama port has the most COVID-19 cases outside of China, with 634 confirmed by late Thursday. Two former passengers have died.
Most crew members and other passengers who have not completed their 14-day quarantines because they had more recent contact with infected people are staying on the ship for now, but they will be transported to a government facility to be quarantined in isolation.
Japan is discussing with the ship operator and home countries of foreign crew members over their future movements, he said.
Six government quarantine workers contracted the virus, raising questions about the protective measures used.
The new coronavirus that causes COVID-19 has sickened tens of thousands of people, mostly in central China's Hubei province.
The U.S. and other countries have put former Diamond Princess passengers in second quarantines. Eleven Israelis returned home early Friday and were taken to the Sheba Hospital near Tel Aviv for quarantine and testing.
"We don't know that (more will test positive), but if they do, we are completely well set up to detect and manage them and isolate them," Murphy said.
Kato said Australia, like the U.S., brought home a mixture of passengers who tested negative and others who were not tested and had an unknown status, therefore it was difficult to know when or how they had contracted the virus.
Kato said passengers who returned home on the U.S. and Australian flights did so before completing the Japanese quarantine process, and that Japan's ongoing disembarkation of passengers is still adequate.