Minister of health Chris Hipkins estimates there could be "a couple of hundred" people affected by the director-general of health's stay at home order for those connected to the cases of Covid-19 community transmission in Auckland.
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"The contact tracing is now under way for all of them. We are taking a very precautionary approach."
At least 200 contact tracing calls had been made by about 4.30pm on Wednesday, he said.
"They are working around the clock. We have 160 people at the call centre making calls as we speak so I imagine it will be done very quickly."
There was capacity to contact trace up to 350 positive cases per day, he said.
Asked about what modelling said about infection rates, Hipkins said: "We are not focused so much on the modelling as we are focused on the testing and the contact tracing. We are basically going to run this thing to ground. We are going to find every person who has come into contact with those positive cases and if any of them test postive we are going to find every person who has come into contact with them. And we are moving at speed to do that.
"The modelling is an interesting academic exercise but far more important is testing and contact tracing because that is actual people rather than hypothetical scenarios."
Asked where the transmission had come from, Hipkins said: "At this point it is a real puzzle. That is one of the reasons we moved quickly last night ... the family concerned have no known links at this point that can be identified with people who are working in managed isolation or quarantine or at the border or who have had recent travel history.
"So that does make it a particularly puzzling question.
"We don't want to see community transmission take off again. The faster we go through this process of testing and contact tracing, the less likely that is."
The virus coming in on imported goods had "not been ruled out" but scientific advice suggested it was less likely.
"We have not discounted that as a possibility ... at the moment there is one cold store site that seems to be the centre of the group at the moment so site visits have been taking place today and that will include testing on site."
As for testing centres, a further six were being stood up in Auckland on Wednesday afternoon and another three at 8am on Thursday.
"We are doing everything we can to scale up testing as quickly as we can. We are asking all GP practices to undertake tests for those who need tests. We want to make sure availability of testing is as wide as we can make it."
He asked for people to be patient while waiting for tests and to make sure they did get a test.
Asked if Auckland could be at level 1 by the weekend, Hipkins said: "I think we will know a lot more by Friday."
He said hypothesizing what might happen on Friday would be "crystal ball gazing".
He did not have the testing numbers for Auckland on Wednesday, but he expected it to be very high.
Up to 10,000 tests or more would be processed overnight, he said.