There are over 340,000 people in the country who are fully vaccinated, and some time next week, it's expected the millionth dose will be administered.
"I am pleased with that progress," Ardern - who will have her first vaccination today - told Morning Report.
Yesterday, she said the country was at "107 percent of target" as she revealed details for the vaccine rollout to Group 4.
The vaccine is currently being delivered to Group 3 - people who are at risk of getting very sick from Covid-19. They must be aged 65 or above and meet other criteria like having an underlying health condition.
In South Auckland, half of those over 65 have not been vaccinated yet, despite being eligible.
Ardern would not answer directly when asked if she was satisfied with that outcome.
Instead, she said: "I want everyone who is eligible to be vaccinated. But I'm not going to give those who may not have come forward yet a hard time."
Group 3 covers about 1.7 million people, and only 34,000 have been fully vaccinated.
"It is a large group of people. There was no sense I think, that we were going to complete that group within a week of opening up eligibility. We are expecting that we will roll through with that group through the course of July as well."
New Zealand has previously been ranked the second slowest Covid-19 vaccine rollout in the OECD.
Recently, the OECD said "The pace of vaccination needs to accelerate to reduce the risk of new outbreaks and pave the way for full border reopening in 2022".
To the criticism of the slow rollout, Ardern said: "We are one of very few countries who have opted to use Pfizer as the vaccine we will use predominantly for all of our population. Not many countries are doing that. That will mean we have different delivery schedules.
"However, most countries, many, many countries, are looking to complete their vaccine rollout in a similar timeframe... It's when you finish that matters, because when you finish you start seeing those opportunities."
No-one should make guesses that border openings would mean all restrictions being lifted and a return to pre-Covid-19 life, Ardern said.
"Looking around the world at the moment, everyone has some form of requirement, whether it is pre-departure testing or vaccination certificates. What a good solid vaccine rollout ... will mean is we can start changing up some of the restrictions.
"We may start looking, for instance, to some low-risk countries and say we may not have the same requirements for quarantine for you that we otherwise might have. So that gives us more options whilst still maintaining the freedom that we have."
As for the level of vaccination that might be able to begin at, Ardern said: "We have asked that questions of a group of experts we have pulled together, led by Professor David Skegg because that is the exact question we are asking ourselves - 'At what point will we have enough people vaccinated that we can feel comfortable changing up some of our systems?'.
"They are working on that for us, so once we have some of the answers we will be shortly making that public."
Contacting eligible people
We have the contact details of about 90 percent of New Zealanders through health providers. And what we are telling people is we will be using ... a national booking system called book my vaccine. So people when they become eligible will receive an email, a text, a phone call, however they usually communicate with their health provider they will get notice.
"That then gives them the ability to go online and book their vaccination."
Those who were not so readily contactable could go online and enter their details into the system so they could be contacted.
There was no cut-off date for vaccinations for those who were available, she said.
When the programme moved on to another group, the group or groups before were still eligible.
"We do want to keep those numbers up, we do want to reach those eligible. Measure of success for me is going to be whether we have vaccinated as many New Zealanders as possible by the end of the year.
"Yes I want everyone who is eligible to be reached as quickly as possible."
