He has also said they want to be vaccinated publicly to encourage take-up.
Australian Prime Minister Scott Morrison received his vaccination at the start of Australia's vaccination roll-out.
Dr Nikki Turner, the head of the independent Immunisation Advisory Centre, said the vaccine rollout in New Zealand did not need to be as fast-paced as in other countries, and there were benefits in a slower programme.
Turner got her first vaccination at a new vaccinations clinic in Wellington this morning.
There has been some criticism about the speed of New Zealand's programme compared to other countries.
Border and MIQ workers are getting their second round of shots now, while first jabs for high-risk people in high-risk settings are scheduled to begin now, people at risk of getting very sick from Covid from the start of May, and the rest of the general public from July.
Turner said there was also no need to rush the rollout, as other countries were doing – and some other countries had come up against problems due to the rush.
"There is no Covid in the New Zealand community so we can do this thoughtfully and carefully. Our rollout should and needs to look quite different from other countries.
We have not got elderly people in large rates dying, and people with medical problems. So yes, we could rush faster, but I think we should do it thoughtfully and carefully and take our population with us.
"Yes, New Zealand might take longer to build up, but it gives us time to put all the appropriate processes in place."
Turner believed the vaccine rollout was going well so far, although she did not have the data on the numbers vaccinated.
"It's never going to be perfect. We are going to see problems, and we expect to see problems. To date I'm not seeing large amounts of vaccine hesitancy or fears."
She said New Zealand is right to put all its eggs into the Pfizer basket, provided the Government can be certain of getting the supply it needs.
"So long as we are comfortable we are getting reasonable supplies of the Pfizer, this is a really good answer. The data is so secure on this vaccine [so] we can feel very confident that it is a highly effective vaccine and it comes with extensive safety data.
"So why would we turn it down?"
She said the best way to respond to those raising concerns about the vaccines was to use science: people understood that it was the best way to protect against the pandemic.
The Government estimates that 5 per cent of the population will refuse the vaccine, while 20 per cent will be hesitant.
It has refused to have a vaccination target, saying instead it wants to vaccinate as many people as possible.
The National Party has called for a target and suggested at least 70 per cent of the population.
Turner backed the Government in simply trying to vaccinate everybody who wanted to be vaccinated, and who had been given good information.
She said that, as yet, there was no known figure at which herd immunity could be declared.
"What's the point of saying 60 per cent, 70 per cent, 80 per cent? What if you got 71 per cent? Do you go home?"
She said her call would be to ensure people from impoverished backgrounds - who had traditionally missed out - were vaccinated along with everybody else.
