Authorities say incoming COVID-19 community test results following the Auckland cases are encouraging, but caution in the next few days will be crucial.
A surge in testing has yet to discover any spread to close contacts or further into the community.
Director-General of Health Ashley Bloomfield told Morning Report that was positive, but it was important for parallel chains of transmission to be uncovered if they existed.
"The key thing we're trying to rule out is, first of all, have any of our existing cases passed the virus on to someone, either at the school or in the workplace. Now the testing so far is reassuring in that case."
The daughter in the Papatoetoe family at the centre of the recent community cases was the first to report the onset of symptoms, but it was still unclear if she was the index case.
"Whilst, yes, the mother works in the Auckland Airport precinct and, whilst arm's length removed, has got an association with incoming flights through being part of that laundry, it's really important here to remain open-minded," he said.
"So, we're very interested, of course, in the testing from the school to make sure that if indeed the daughter was the index case that we are identifying where that might have come from."
The mother, father and daughter - who all tested positive - have been moved to quarantine, while another household contact who has tested negative remains in isolation at home. Bloomfield said the family was doing well.
More than 3000 people were tested across the Auckland region on Monday, focusing on close contacts and those who had visited places of interest.
"This is the thing we're trying to find out, really are there parallel or onward chains of transmission in the community. I should say that our sense is that we would have picked up at least someone else, through the regular testing of anyone with symptoms," Bloomfield said.
Wastewater testing in the area last week had also returned an encouraging result.
"ESR has been doing some quite regular wastewater testing, the last result from that was on the 10th of February and that didn't show any virus in the South Auckland area."
More wastewater testing would be carried out this week, he said.
On saliva testing, Bloomfield said this was being rolled out across some managed isolation and quarantine facilities and cost around the same as a nasal swab test.
"We have talked to Rako [Science] about their testing, which is saliva based, and the results they have are from the US, which we're still treating with some caution about whether it's going to be as accurate as the swabbing," he said.
"So we will be watching with interest any further work they do and any results they have from that."