Chris Hipkins says officials are having to spend "quite a lot of time" stopping the spread of not just COVID-19, but rumours and conspiracy theories.
Speaking to Newshub Nation on Saturday, the Minister of Health said they're sparked by locals finding out about cases in their communities before the public at large, then going on social media.
"As soon as there's a positive case we start the contact-tracing process which means that news will spread within a local community about that positive case," Hipkins told host Simon Shepherd, after being asked about new revelations of a confirmed case at the University of Auckland.
"We're not speaking about each individual case publicly until one o'clock each day because as soon as we do speak about them, we want to be able to answer all of the questions around them.
"Local communities will know, but there's also a lot of rumours around out there as well... We've spent quite a lot of time dampening down rumours about positive results in Wellington, Christchurch, Queenstown, and so on. So my message to everybody - the authoritative message - is at one o'clock every day."
The National Party has been accused of stoking conspiracies around how the virus re-emerged in New Zealand, and when the Government knew about it.
Deputy leader Gerry Brownlee admitted on Friday he got into a "bad spot" with his line of questioning, which involved suggesting it was "very puzzling" health experts had started talking about the potential inevitability of a new outbreak, the Prime Minister's visit to a mask factory and Director-General of Health Ashley Bloomfield's test for COVID-19, even though he wasn't showing any signs of being infected.
"I, more than most, know what it's like to deal with conspiracy theorists and I'm just not at all comfortable that I might have in any way unleashed some sort of credence to those people because there is no credence in conspiracy theories," Brownlee told Newstalk ZB.
National Party leader Judith Collins, appearing on Newshub Nation after Hipkins, said Brownlee "wasn't trying to spread any conspiracy theories".
"He wasn't the one saying conspiracy theories - others were picking that up and deciding to call it that. But we are getting a lot of information from the public, and we don't have - because we're not the Government - a way of actually getting that verified, other than looking at it and saying, this is possibly something we should send through to the Government to check out. That's what we're doing now.
"Gerry was simply reflecting what he had been hearing and the level of anxiety in the community."
She denied Brownlee's reflections would have fueled interest in an anti-mask protest reportedly planned for Auckland on Saturday afternoon.
"He very much regrets any thoughts he might have done that. But he hasn't done that.
"What we're seeing is very different theories coming out... people with very detailed information. We've got no way of checking it out."
Despite shutting down suggestions National is spreading conspiracy theories, Collins said it was "pretty clear" the new outbreak was caused by a leak at the border, as Deputy Prime Minister Winston Peters suggested to an Australian news outlet during the week - despite no proof to date being found.
"It's clear that this is something that has come in either from the UK or Australia. This is not something that was lurking in the community... It's come in through the border in some way."
While genome testing has indeed found the virus that infected the cluster is similar to those circulating in the UK and Australia, no links have been found between it and confirmed cases found at the border.
"There's no evidence to suggest this has come through the border in a person-to-person contact way," said Hipkins.
"That is a real part of the puzzle... We're trying to solve that puzzle as quickly as we can.. It's most likely to have originated in Australia or the UK, but at this point we still don't know how this cluster came into contact with COVID-19 in the first place."
Testing is being done at a cool store, where the first new case of the cluster was dated to July 31, by MPI and police. No earlier cases have been found in the hundreds of people traced and tested to date.
"That's reassuring on one level because it does mean that if this is the only case, then actually we will be able to contain that, we should be able to contain that with the contact tracing and the testing we have been doing," said Hipkins.
"Early days yet - we're only three days into this - but it looks like we got in early, which of course is always our goal."