Chris Hipkins says the reason many people in priority groups for a COVID-19 vaccine haven't got one yet is because they simply haven't come to get one.
While the Government has frequently boasted the rollout is ahead of schedule, documents obtained by Newshub earlier this week showed just over 60 percent of a group labelled 'high-risk' by the Government are yet to receive their first vaccination, and only half of another group - also high-risk - have had their first shots.
And on Saturday the NZ Herald reported 3800 border workers are still yet to get their first jab, as are half of their 50,000 or so household contacts.
"Having them vaccinated at the frontline is critical to maintaining elimination because it sets up a safety barrier at the border," epidemiologist Michael Baker told the paper.
Hipkins, the COVID-19 Response Minister, said there has been a "real emphasis" on the border workers, many of whom are required to get vaccinated or find another job.
"In terms of the families, that's a challenge because it's voluntary," he told Newshub Nation on Saturday morning. "They need to come forward... not all of them have been coming forward."
Director-General of Health Ashley Bloomfield told NZ Herald not everyone who's a household contact would be "coded" in the system as such.
"A lot of effort went into the first four to six weeks to both identify and reach out and actually take vaccinations out to those communities where these people were, but they just won't be coded in the system as identifiable in that group of household contacts."
New Zealand initially ordered four different vaccines, but in January decided to base the entire initial rollout on the Pfizer-BioNTech jab, which has proved to be effective with minimal risk of side-effects. That slowed the rollout somewhat, with other countries also keen to get their hands on it.
"We're doing very well in terms of vaccinations based on what we've had delivered. Our vaccination campaign continues to ramp up - we did about 23,000 the day before yesterday... but the big constraint that's stopped us ramping up is supply."
Newshub on Friday reported some older New Zealanders in 'Group 3' of the Government's COVID-19 vaccination rollout likely won't be immunised until August - or possibly later.
"We've always said there would be overlap between the groups," said Hipkins. " Our key group, group one, which is where the biggest risk is - our border workers and so on - we've put a real emphasis on getting through that."
A recent ranking of each country's COVID response saw New Zealand placed first among the world's major economies, but at risk due to a slower vaccine rollout than many other developed nations, such as Singapore, Israel, the UK and US.