The Delta variant has been identified in 11 of 21 international crew on the Rio De La Plata container ship off the North Island port city.

None of the crew took shore leave, but more than 90 port workers went onto the ship while it was at berthed at the port for four days last week.

Those workers are now being urgently tested for the deadly virus, with 23 negative results received as of 4pm NZST, and further results expected later on Monday.

Should any test positive, it would be New Zealand's first community case since February.

Showing up lax rates of vaccination, Prime Minister Jacinda Ardern revealed just 11 workers have received their first dose of vaccine despite being eligible for months.

"We have encountered a range of barriers (to vaccination) ... that includes misinformation, hesitation," she said.

"We want everyone who's in a high-risk situation to be vaccinated. We've done everything we can to make sure that is happening."

New Zealand will block unvaccinated individuals from working at port sites from later this month.

COVID-19 Minister Chris Hipkins admitted those numbers "were too low".

"We need to have a clear look at whether things should have been done differently including whether New Zealanders should have been able to go onto that ship," Mr Hipkins said.

On Monday, Ms Ardern also announced vaccine eligibility would be extended to people aged 50 and over from this Friday.

Around 35 per cent of adult Kiwis have received one dose, and one in five are fully vaccinated.

New Zealand is vaccinating around 190,000 Kiwis a week, and Ms Ardern is holding firm to a commitment of vaccinating every consenting adult by the end of the year.

Australian Associated Press