"We've also told them that if they do not choose to travel on this flight, they will need to undertake a quarantine in Japan before they come back to New Zealand."
She understood the frustration they would be feeling after having already been in isolation for 14 days.
"But unfortunately there has been such a rate of transmission, despite some incredible efforts from all those involved, that we do need to put public health and their health first and undertake a further quarantine."
She said there were some people on the ship who were very distressed and eager to get back to New Zealand and the current quarantine facilities at Whangaparaoa were giving good care to New Zealanders who had returned from Wuhan in China.
Asked if the Government could compel New Zealanders in Japan to go into isolation, Ardern said : "Actually we can say at the border that they will not be able to board so yes, we can take those measures but actually I feel confident we are giving options here. We are giving people the ability to come home and that's important.
"But if they choose not to, we need to keep in mind that if they choose to fly commercially it then exposes a range of other people to risk."
The best option was to come back. If they chose to stay they would need to wait another 14 days.
The Diamond Princess has been in lockdown in Yokohama for about a fortnight with about 3700 passengers but the virus has spread.
About 16 Australians and two New Zealanders have the virus and have been hospitalised for treatment.
The United States has evacuated 300 of its citizens who were on the boat, including 14 whose positive tests for coronavirus came through after they had disembarked.