The two community cases of coronavirus in Christchurch weren't using the COVID Tracer app, with Chris Hipkins as yet unable to say where in the city they might have visited.
But the COVID-19 Response Minister told The AM Show on Thursday moving the city into a strict snap lockdown is "unlikely" - although he wouldn't rule it out.
"We don't have enough information, at this point, to make a good, robust assessment of the level of risk in Christchurch.
"They've been back in Christchurch for about a week - they could well have been infectious for quite a proportion of that period. They've been quite unwell.
"My understanding is there's at least one other household where there's likely to have been close contact so they'll be working to chase that down very quickly."
The Ministry of Health confirmed the Christchurch cases on Thursday morning, with one of them having recently returned from Auckland and the other a household contact.
"I was informed of the cases late last night; both unvaccinated people, one of whom was in Auckland," Hipkins said.
"From my understanding, it was an authorised trip to Auckland that involved the care of a child.
"They had a negative pre-departure test before they left Auckland."
Hipkins said the cases "weren't scanning" with the COVID Tracer app.
"I don't have, at this point, know the extent of their movements - whether they'd been out shopping or out and about in the community but the interviews had started late last night - they'll be continuing this morning. That will help to get that information then we can make a proper assessment of the level of risk in Christchurch."
Hipkins said it was too soon to say much else.
"This person did have a test so the system worked as it should. The reality is when you're dealing with a virus, it is impossible to absolutely eliminate all risk and this is one of the reasons that the whole country [outside Auckland and Waikato] is at alert level 2.
"We've been aware that there's a possibility of cases popping up in other parts of the country. Alert level 2 helps in the sense that it reduces the potential exposure that can flow from those cases.
"This is the reality that we are in, in New Zealand. COVID-19 Delta is here - it is impossible to seal a border around Auckland - people do need to come and go from Auckland."
Hipkins said the Government was doing everything to minimise the risk.
"The reality is that, regardless of how tight you make the boundary around Auckland, it is going to be impossible to absolutely guarantee that no cases will flow from out of Auckland.
"This person had a negative test before they left Auckland in the 48 hours before they left… and still managed to be incubating the virus.
"I just want to be clear about this, there is no way to guarantee that the virus won't make its way out of Auckland - and anyone who says that it's possible to make that guarantee is not telling the truth.
"Delta is here in the country and it is a question of when, not if, it makes it into other parts of the country and the best defence we've got against that is for as many people as possible, wherever they are in the country, to get vaccinated."
Hipkins wouldn't rule out using alert level 4 in Christchurch.
"I think level 4's certainly unlikely. I'm not ruling anything out, though."
Hipkins is scheduled to front a press conference at 1pm with the latest on the Christchurch situation and all other COVID-19 developments.