The victims, Australian and UK citizens, were working for a Norwegian aid agency.
The border has been shut since the re-emergence of COVID-19 in the community in New Zealand.
They were missing at sea for three days.
All travellers on board the MS Paul Gaugin have been forced to isolate in their cabins.
Decades of research in archaeology, linguistics and genetics now show that Polynesian origins lie to the west.
"Jacinda, why you are so reluctant to let us travel to and show our support for the Cooks?"
The name Cook Islands has been criticised by some for a lack of history.
Pasifika leaders are worried their illegal status could put the country at risk for transmitting COVID-19.
"You're restricting your own citizens and you're also restricting your friends."