If that did not work out, she said the rollout could have to be pulled back to that 350,000 a week level to avoid running out of vaccines before the big supply drops from October, when about four million doses are scheduled.
She also did not rule out measures to try to keep Auckland being vaccinated at surge levels by delaying new bookings in other regions.
Ardern said one of the issues being looked at was whether it was possible to meet all existing bookings in other regions while keeping Auckland at the current high rates.
The Government had included South Auckland as a priority area for early vaccination, but had not widened that to include wider Auckland.
The Government has come under pressure over the rollout after Covid-19 Minister Chris Hipkins first revealed that the supplies might not keep up with the pace over September.
In May, Hipkins told Heather du Plessis-Allan on Newstalk ZB 10 million doses ordered from Pfizer would arrive in the country at the end of the third quarter - end of September.
"We will get them all by the end of the third quarter, so September," he said.
Last week, after indicating vaccine supplies could run low over September if the lockdown surge levels were maintained, Hipkins told du Plessis-Allan he had actually got the date wrong, saying he'd been told "by October" when actually it was meant to be "the end of October".
"I was advised that agreement had been reached with Pfizer for all our vaccines to arrive by October, which I interpreted to be in the third quarter," Hipkins said.
"I was subsequently advised the delivery schedule was through to the end of October. I accept that my statement at the time was not totally correct."
However back in June, Hipkins told du Plessis-Allan again that all of the Pfizer stocks had been due to arrive by the end of September, but the Government had asked Pfizer to delay some of those shipments so they were staggered over October and November as well.
At the time, Hipkins said that was to ensure New Zealand didn't end up with a big stockpile which potentially would expire before it could be used.
"Yes they have indicated to us they will continue to meet that delivery.
"We are talking to them about if some of that should be over October and November to make sure that we are smoothing the deliveries so that we don't end up with a whole lot sitting in the freezer.
"We will talk to them about making sure we don't end up running the risk of having doses expiring before being able to use them."
Today Hipkins told the Herald in a statement the point he was making was that at the end of the programme there were expected to be doses leftover.
"To smooth them out towards the end of the year would give us more options into next year," he said.
Te Pāti Māori co-leader Rawiri Waititi said given Tāmaki Makaurau, Auckland, was the centre of the outbreak it needed to be prioritised in the vaccination programme.
Given the higher vulnerability to the virus, Waititi also urged providers to prioritise Māori and Pasifika, who are also being vaccinated at rates much lower than the national average.
"This virus is entering our country via Tāmaki Makaurau and it is being carried to the rest of our regions from there," Waititi said.
"If we want to protect our people, we need to begin there. Aotearoa will never be safe until Tāmaki is safe.
"It's no secret that Māori and [Pacific Islanders] are the most vulnerable communities and they make up the largest concentration of our people living in Tāmaki so we need to put a pou in the ground and put our people at the front of the queue."
