Covid-19 Response Minister Chris Hipkins says 66,296 doses of the Pfizer vaccine have been administered as of last night.
About 52,183 New Zealanders had received a dose, while 16,483 had received both, Hipkins said at a media update this morning.
For the next couple of months he expected 7000-8000 people to be vaccinated each day.
The Government aimed to ramp up to 50,000-60,000 vaccinations a day, Hipkins said.
From July, vaccines would be arriving in the country faster than they could be administered, so the Government had to be ready for the mass rollout.
There were more than 50 sites administering vaccines, and vaccination of border workers was progressing well.
The Government had been hitting about 96 per cent of its delivery target so far, Hipkins said.
Rapid courier services would be used when the mass vaccination rollout began so vaccines could be moved around to where they were needed most.
Within the next week the Government would start to release more regular updates on the number of people vaccinated.
First ministers vaccinated
Hipkins also received his first dose of the Pfizer vaccine this morning, as did Associate Health Minister Ayesha Verrall.
After his jab, Hipkins said he "didn't even feel it".
He had chosen to have his jab in public to help instil confidence in the vaccine. "We are concerned about the degree of misinformation out there. That's one of the reasons I've done it today.
"Making sure that people are getting their information from trusted sources is really, really important."
Verrall said she was excited to be getting the jab. "If we all go through with the vaccine the whole community will be protected."
She noted it would not change anything for her for now because she wouldn't be fully protected until after the second dose.
It follows the release of a review into the Government response to the August outbreak last year, which said it was too reactive, lacked clear lines of accountability, and didn't seek enough expertise outside the health sector.
Speaking about the review into the handling of the August cluster, Hipkins said the Government was always looking to improve its processes.
Hipkins said they were about to test the contact tracing system the week the August cluster broke out.
The minister was expecting more advice on pre-departure testing to understand whether it was effective and was being carried out correctly.
About 800 Covid cases had come through MIQ facilities in total. Hipkins said managed isolation facilities would be needed until the end of the year at least.
Last week's vaccine update showed that 41,500 people had received the first dose of the Pfizer vaccine, and 500 had had both doses.
The National Party has questioned why the Government isn't releasing daily vaccination numbers, but on Monday Prime Minister Jacinda Ardern said that would only happen when the rollout to the general population started in July.
This month, Hipkins said that about 6000 to 7000 doses should be administered daily by this week.
National has also called on the Government to adopt a vaccination target, but Hipkins has said the goal was simply to vaccinate as many people as possible.
The rollout has not been without its issues. It has been criticised as too slow compared to other countries, but Dr Nikki Turner, the head of the independent Immunisation Advisory Centre, said it didn't need to be as quick as in other countries, nor did there need to be a vaccination target.
Meanwhile, a sweeping review of the booking system is under way after a data breach exposed the personal details of more than 700 people.
And yesterday the Ministry of Health's northern coordination centre apologised after it ran out of vaccines by lunchtime and those with appointments missed out - even though some walk-ins were able to get a jab.
Yesterday Hipkins said Government ministers with health or Covid-related portfolios would be the first Labour MPs to be vaccinated, with himself and Verrall first.
MPs from other parties with similar portfolio responsibilities were also invited to be vaccinated early.
Hipkins has said that it was a balancing act to decide when to vaccinate ministers as they wanted to encourage up-take, but didn't want to be seen to be queue-jumping.
It remains unclear when Ardern will get vaccinated.
Border and MIQ workers are now getting their second round of shots, and 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 public from July.
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."
The Government estimates that 5 per cent of the population will refuse the vaccine, and 20 per cent will be hesitant.