"Māori are not particularly finding the process of getting vaccinated easy and that's why initiatives like Te Whānau o Waipareira out in west Auckland make a difference but this takes time."
The availability of places to get vaccinated was still very restricted in some areas, Tukuitonga said.
"There is also an element of people who are hesitant or uncertain as well as hardcore anti-vaxxers who won't get the vaccine."
The fact that younger age groups had only recently become eligible for the vaccine was also contributing to the slow process, he said.
Deputy Prime Minister Grant Robertson said there was a big focus on Auckland for the rollout, but the plan was for a national rollout.
He said there was no shortage of vaccine in Auckland - and emphasised that people could get a vaccination this weekend if they wanted to.
A surge in people getting vaccinated had come during alert level 4, when it was a major focus, Robertson said.
"That had dropped off a bit since most of New Zealand dropped to level 2," he said.
The Herald can reveal a breakdown of each district's vaccination coverage using the latest Ministry of Health data, as of 11.59pm on Tuesday, September 7.
In the Auckland region, Counties Manukau DHB - which represented south Aucklanders - had the highest rates of fully vaccinated people - 37. 2 per cent, which equated to 179,807 people.
But the district's progress seemed to be slowing, with 26.3 per cent having received one dose and 36.4 per cent (175,905 people) who remained unvaccinated.
The Herald asked Counties Manukau DHB for comment and was awaiting a response.
In comparison, Auckland central had less people (34.9 per cent -147,792 people) fully vaccinated but far fewer were unvaccinated (30.7 per cent -129,966). The remaining
34.5 per cent had received one dose of the vaccine.
Waitematā DHB - representing people in north and west Auckland - had the lowest rates in the region and sat below the national average.
The number of fully vaccinated people in the Waitematā district was 158,785 (30.2 per cent) - the national average was 33 per cent. And 37.5 per cent (197,388 people) were unvaccinated, with the remaining 32.3 per cent having received one dose.
A Waitematā DHB spokeswoman said this was because the two other Auckland-based DHBs started their vaccination programmes four to six weeks ahead of Waitematā DHB, as the focus was on priority groups within their areas, such as border staff.
"There are no MIQ facilities, major ports or airports within the Waitematā catchment, meaning vaccination began later in our district," she said.
"If you were to compare our current progress, in line with the other metro Auckland DHBs four to six weeks ago, it would demonstrate that the Waitematā vaccination rate is ahead of the other metro Auckland DHBs," the spokeswoman said.
Immunisation Advisory Centre director and GP Dr Nikki Turner, who advises the Government on vaccines, said from where it was a few months ago, Auckland had made huge progress - but there was still a long way to go.
"We are planning to ensure every New Zealander has this year been offered ease of access to a vaccine and when we have achieved that and feel like all communities have had fair access, then we have done everything we can," Turner said.
She said it would be lovely to see more than 90 per cent of the country's population vaccinated, but there was no magic figure.
"We don't want to leave communities behind so it's really important we don't see equity gaps in age groups, by ethnicity, by levels of poverty, that the importance of ensuring all the New Zealand communities is included, is as important as the absolute number."
She said vaccination services were doing very well, there was a good vaccine supply and for that reason Auckland did not need to be prioritised over the rest of the country.
"If we had a supply shortage then that would be a consideration but because we have been able to get in the extra supplies, we don't want to lose the momentum anywhere in New Zealand."
Nationally, Bay of Plenty was the worst performer with nearly half its population (47 per cent) still to be vaccinated.
Taranaki wasn't far behind with 46 per cent not having received the jab, and Lakes DHB - which represented people in Taupō and Rotorua - had 45 per cent or people unvaccinated.
Nelson Marlborough DHB was leading the way with 42 per cent of eligible people fully vaccinated, while 31 per cent had received their first dose and 27 per cent were unvaccinated.
Southern and Capital and Coast DHBs had the least number of people left unvaccinated, both sitting at 29 per cent.