There are no new positive cases in the community - and there are four cases in managed isolation, director general of health Dr Ashley Bloomfield says.
Bloomfield said the lack of new cases was encouraging but stressed "we're not out of the woods".
There were 8880 tests processed which mostly would have been taken on Sunday.
Bloomfield said they were expecting high numbers of swabbing again today and tomorrow.
Bloomfield said even with another day of zero cases, he was still confident in the lockdown and wasn't concerned about the ability to enforce and justify alert level 3 because there were so many high-risk exposure events.
There are 11 community testing centres open again today and people who are symptomatic or at one of the exposure events should be the ones getting a test - anyone else should stay home and can call Healthline for more advice if needed.
The most important thing Aucklanders can do to stop the spread of the more infectious UK variant is to stay home as much as possible.
Bloomfield thanked Aucklanders who are doing this for the greater good and are putting that ahead of their circumstances.
On lockdown exemptions, almost none are being granted for weddings and a limited number are being granted for immediate family members for funerals and tangihanga.
Of the 1855 people at Papatoetoe High School - all bar four have had at least one test result and the others are isolating.
About 50 are waiting for their second test results.
Of the 21 close contacts of Case M at MIT, all tests are so far negative.
More than 4000 calls were taken by Healthline with more than half being Covid-related calls. The average wait time was 26 minutes. Bloomfield reminded Kiwis wanting general Covid information to look on the ministry website.
Bloomfield said he didn't think there was any inconsistent communication at Papatoetoe High School, when asked about messages to Case L.
Case L, a sibling of a student at the school with Covid-19, went to work at KFC in Botany Downs before she tested positive for the virus herself.
Bloomfield said the latest cases were a reminder about what can happen when we don't follow advice.
"What has serviced our country well over the last year is everyone doing their bit."
He was concerned prosecutions would deter people from coming forward.
"It's frustrating about what has happened in this instance is that it's had such an impact."
Bloomfield said the vast majority of students and staff understood the message.
The original source of the infection is still a mystery with two equally unlikely scenarios - that it was connected to a December case in MIQ without any evidence of community spread or that it's connected to the family through the mother's work at the border but without there being a clear path of transmission. The daughter also developed symptoms first and Bloomfield called the hunt for the source "puzzling".
Bloomfield told Newstalk ZB's Mike Hosking he was looking for zero days of community cases to determine when Auckland's lockdown should come to an end.
One of the cases which sparked Auckland's lockdown had been about for a week while infectious and the last exposure event was Saturday so those cases might not show up until mid-week.
He said he wasn't getting the police involved so far this lockdown because the families needed support to navigate isolation.
"In the first instance we get our health providers to go out because often what it is the families just need support to stay isolated safely. If we have any issues or challenges or if we can't find people then we don't hesitate to involve the police."
He said he did not think a punitive approach was the best way to counter the virus and get people on board.
Bloomfield imagined the MIT student who sparked this lockdown "wasn't having a great time" at the moment.
"I imagine he's extremely remorseful at the moment. It's a pretty heavy burden to bear."
Prime Minister Jacinda Ardern said the rulebreakers' actions were not tolerable.
"If there is any question mark over there being consequences – those individuals are facing the full judgment of the entire nation."
The Government was this morning criticised for its Covid-19 messaging.
Pasifika Medical Association chief executive Debbie Sorensen told RNZ official terms such as "casual plus contact" were hard to grasp.
"We need to encourage people and reassure them that nothing bad will happen to them if they get tested.
"A lot of people in South Auckland are in casual employment, they're working day by day, and they're very fearful. If that's your only form of income to support a number of people in your household, then the drivers are very strong to actually go to work.
"And so, I think, understanding the context in which people live is actually the heart of the matter."