Covid-19 Response Minister Chris Hipkins said there have been more than 388,000 vaccines administered across New Zealand. 120,000 of those have had their second doses.
Director-general of health Dr Ashley Bloomfield said there is one new Covid-19 case in MIQ - none in the community.
Bloomfield said the current assessment of the public health risk to New Zealand from the community case in Melbourne is low.
He said officials have advised quarantine-free travel can continue.
Yesterday there were 14,000 doses of the Covid-19 vaccine administered and things are tracking ahead of the planned rollout.
Hipkins said the Government will hit the half-million mark within the next fortnight.
He thanked the workers across the country who are "delivering really good results".
In the last week, Auckland tipped over the 150,000 mark when it comes to Covid-19 jabs.
More than 80,000 people got the Covid vaccine in the past week, Hipkins said.
He said the Government's booking system is working well ahead of the national vaccine rollout.
He said the vaccine rollout was an "evolving process" and the Government will continue to "refine" its logistics.
He said in the early stages there will be "teething troubles", particularly at the bigger and busier centres.
Hipkins had a message for people in group 4 - people aged under 65 and without any underlying health conditions - please refrain from walking up to a vaccination clinic at this stage.
That is because people who do have a booking might miss out, and people in groups 1, 2 and 3 must be prioritised for now.
People booking in first will help avoid people missing out and reduce congestion.
Asked how chaotic the walk-ups have been for the vaccination centres, Hipkins said this has been limited - but the Government is wanting to limit this happening.
"Everyone wants one - which is great," Hipkins said.
But the Government does not have the demand to vaccinate everyone all at once, hence why he is warning against walk-ups at clinics.
Hipkins said a lot of the vaccine hesitancy has been "eroded" in recent weeks.
Asked if the DHBs should be turning people away, Hipkins said that was up to the people running the clinics.
But he said he does not want to see vaccine wastage.
Bloomfield said there will be new vaccine data on the Ministry of Health website that will include an age and gender breakdown, as well as information on ethnicities.
As there are more women in the health sector workforce far more women have been vaccinated than men.
Asked if there needs to be a bigger push to get more Māori and Pasifika people vaccinated, he said the Government needs to do better there.
But he said the reason it's so low for these groups at the moment is that there aren't as many Māori and Pasifika people working in the health sector - that's the group which has been targeted for vaccines first.
"We've got to do better - there is no question about that."
Medsafe is expecting data from the US on giving the jab to 12-15 year olds and the Government is already preparing how to manage this, if it does get approved.
Bloomfield said people can sometimes have reactions to the vaccine and it does have side effects - many are mild.
But serious reactions do happen - and the Government is monitoring these through the Centre for Adverse Reactions Monitoring (Carm).
The deaths of three elderly people in the days or weeks after receiving the vaccine were referred to Carm for investigation and health officials were confident they were unrelated to the vaccine.
Today's update comes as the Government faces pressure over the operations of some of its vaccine sites – specifically one in Auckland.
The Herald reported that one site was described as a "shambles" after an 81-year-old was turned away from her pre-booked appointment when the site closed temporarily yesterday due to a lack of space.
Wendy Carpenter and her mother Robin Cornish arrived at the Highbrook site just before the 11am appointment yesterday to find a long queue of cars stretching along Highbrook Rd.
But, despite waiting in a queue for nearly half an hour, they were told the site had to close due to a lack of car parks.
"[It's] frustrating, it was a shambles," Carpenter told the Herald.
"It didn't look organised or in control at all to me."
Hipkins' message to Kiwis overseas
Hipkins said there a number of MIQ spots available currently.
"Now is a good time for NZ citizen and permanent residents wanting to come to New Zealand," he said.
"If you're a Kiwi wanting to get home, do it now."
He said it was "comforting" that he can now quite publicly tell Kiwis that they can come home now.
He said the availability of MIQ may change with seasonal trends and the Government "did what it could" during those high-demand periods.
Community case in Melbourne
The Melbourne case is linked to the Australian border, Bloomfield said, and the risk to New Zealand is low.
He said anyone who was in any of the locations of interest in Australia is not allowed to travel back to New Zealand for 14 days.
There were 4,500 people who have travelled to New Zealand since the case was in the community, which was on May 6.
Hipkins said Australian health officials will start to identify people who are casual or close contacts of the case in Melbourne, and that information will be provided to the Ministry of Health.
Vaccine stockpile expected to run out in June
The Government "fully expects" to have used all its vaccine stockpile by the end of June.
If it looks like the Government might run out before then, Hipkins said he will ask officials to "slow down" the process.
That stockpile is 350,000 as of last night.
But he said that number drops down week-on-week. In July, he said the Government will receive a "big" shipment from Pfizer.
He said he was highly confident that this timetable will be met - "when Pfizer says they will do something, they do it."
Hipkins said Pfizer has not indicated that the situation in other countries, such as India, has changed the vaccine delivery timeline.
He spoke very highly of Pfizer, saying they stick to their agreements.