Since August 12, the Ministry of Health's contact tracing team has identified 3912 close contacts of cases - of which 3908 have been contacted and are self-isolating.
Health officials said: "We are in the process of contacting the rest."
Of those active cases, 33 are imported cases in managed isolation quarantine facilities around the country.
A total of 37 people are community cases.
The zero cases reported today and with seven people deemed to have recovered from the virus, New Zealand now has 70 active cases of Covid-19.
The total number of confirmed Covid cases remains at 1458 and is the figure that has been reported to the World Health Organisation.
Laboratories processed 7360 Covid-19 tests yesterday. That brings the total number of tests completed to date to 897,077.
Yesterday's cases
It comes after seven new positive cases were announced yesterday at the border.
All of those cases were of people in managed isolation facilities around the country and were of returning residents or citizens who had recently arrived from India, Uzbekistan and Indonesia.
None of the cases were within the community or, more importantly, linked to the latest Auckland cluster.
The latest community case is a girl, under 10 years old, who tested positive for the virus on Monday and is linked to the Botany sub-cluster.
The youngster is a close contact of a person who had tested positive for the virus earlier and, as a result, had been in isolation since August 30.
The mandatory 14-day quarantine period had just finished on Sunday when the girl and three other close contacts were dropped off at Chapel Downs Primary School on Monday morning, about 8.30am.
About 9am, however, all four were picked up from the school grounds after the family was notified that the little girl had tested positive for Covid-19.
The fact the pupil had been at school on that day, albeit very briefly, was only made known to the school on Wednesday afternoon.
As a result, the school - in Flat Bush, South Auckland - has been closed down by health authorities until at least Monday; as it is cleaned and close contacts are identified and contacted.
The Auckland Regional Public Health Service has spent the last few days contacting those deemed to be close contacts of the child. However, that number was said to be "very small," authorities said yesterday.
A Ministry of Health spokeswoman told the Herald today that the child's family was told she had tested positive for Covid-19 at 8.39am on Monday.
"This timeline means there was a period on Monday morning when the family would have been unaware of the child's positive result.
"That is when the child – who was asymptomatic - was briefly on the school grounds but was picked up following notification of the result," she said.
"As soon as formal notification was received, steps were taken to alert the family and the appropriate contact tracing and interviews took place."
There have been three deaths related to the Auckland August cluster - Dr Joe Williams and brothers Alan and Nigel Te Hiko.