"Repeated, deliberate and malicious spread of misinformation" is threatening to block a move to alert level 1, Health Minister Chris Hipkins says.
Hipkins' comments follow health officials revealing four new Covid-19 cases today, two of which are in the community.
The other two are border cases in managed isolation.
Both of the two new community cases are linked to the Mt Roskill sub-cluster, which was sparked when an infectious member of the Mt Roskill Evangelical Fellowship Church visited the home of a bereaved family.
The person was unaware they had Covid-19 at the time of the visit.
Hipkins said officials were moving as quickly as possible to contain the sub-cluster, but "repeated, deliberate and malicious spread of misinformation" was threatening to block a move to level 1.
"We can all play our part in drowning out misinformation by sharing the right information."
He said people should accept the science, and events globally showed how serious Covid-19 was.
Pasifika and Māori public health officials were supporting the Mt Roskill mini-cluster, and ministerial colleagues Peeni Henare, William Sio and Jenny Salesa have engaged with the community on behalf of the Government.
There are 101 close contacts associated with the sub-cluster, and compliance was being monitored more stringently than normal, including home visits by health officials.
"We're getting a very, very good rate of compliance," Hipkins said.
There appeared to be no reluctance from church members to be re-tested, he added. Almost two-thirds of the 332 people in the congregation had been retested by 8am today.
He said using powers under the Health Act to force people into quarantine was always an option for uncooperative people suspected of being a public health risk, but it was far more preferable to share good information to encourage compliance.
Some of the people in the sub-cluster were in the community under the looser level 2.5 restrictions before they were identified as close contacts, but Hipkins didn't have detailed numbers.
He expected more cases in the sub-cluster but it appeared to be contained because all the recent positive cases were close contacts who were already isolating.
Moving to alert level 1 after September 16 was a decision for next week, he said.
Penalty for illegal meetings?
Asked about penalties for those who had broken lockdown rules, Hipkins said it was more important to support people's cooperation rather than taking a punitive approach.
"Come forward if you've got concerns, get a test if you're worried. There won't be a punitive approach here."
He hasn't looked at whether there were criminal sanctions for people spreading misinformation, but it could be looked at if it became more of a problem.
"We can give the misinformation nowhere to go, just as we give the virus nowhere to go. That's the best safeguard."
The importance of identifying close contacts was underlined by the case of the St Dominic's student, he said, who was a contact of a close contact who had been previously undisclosed.
Whether that non-disclosure was deliberate was still unknown, he said.
Asked about lockdowns in suburbs, which National's health spokesman Shane Reti has raised, Hipkins said they didn't work in Melbourne and they wouldn't have worked with the Auckland outbreak.
That approach in Auckland would have led to the same explosion in case numbers as Melbourne experienced, he said.
Tests of Mt Roskill church members
The Ministry of Health said church leaders at the fellowship were encouraging members to get re-tested by Friday and to comply with health advice such as self-isolation.
There is an additional testing station at the Mt Roskill War Memorial, which is open from 9am to 4pm.
"This sub-cluster has come about as a result of a contact of a case having close contact with other people," the ministry said.
"As far as we can tell they were unaware they had been infected and were incubating and spreading the virus at the time.
"This underscores the importance of close contacts following the public health advice they're given which includes strict self-isolation even if they don't have symptoms, and even if they have returned a negative test."
There are also pop-up testing stations that can move to new locations to respond to community need.
The new imported cases are a man in his 30s and a woman in her 50s. Both cases arrived in New Zealand on a flight from India on August 27.
They were in managed isolation in Christchurch and tested positive to day-12 testing. Both cases are now in quarantine.
The case at Auckland high school
The ministry said the deep-clean of St Dominic's Catholic School, where a student who is part of the sub-cluster tested positive, has been completed.
Many members of the school community have been tested since they were informed of the case on Tuesday afternoon.
Testers have been supplied with a surveillance code for testing of asymptomatic members of the school community so it can keep track of the numbers.
As at 11am today, labs had registered 561 tests against this code.
Staff and students have been provided with access to two dedicated testing centres so they don't have long waits.
The vast majority of students at St Dominic's are casual contacts, and being tested as a precaution. If these students and staff are well and have no symptoms, they do not need to self-isolate while waiting for test results.
There are now 72 people linked to the wider Auckland cluster at the Jet Park Hotel in quarantine, which includes 56 people who have tested positive and their household contacts.
There are now 3372 close contacts identified with the current outbreak, of which 3354 have been contacted.
There are three people in hospital, including two in ICU at North Shore and Waikato hospitals.
With today's four new cases and nine additional recovered cases, the total number of active cases is 120. Of those, 39 are imported cases in MIQ facilities, and 81 are community cases.
Yesterday there were six new cases, all connected to the Mt Roskill Evangelical Fellowship Church.
They were all cases that are part of a sub-cluster of the church group, which was sparked when a Covid-infected church member went to the home of a bereaved family on August 27, when Auckland was in alert level 3.
It is unclear if the visit was against the level 3 rules.
Police had already cautioned church members over an illegal prayer meeting, which was against level 3 rules, on August 15.
Yesterday, director general of health Ashley Bloomfield asked the church members to all be re-tested for Covid-19, along with people who associate with them.
He conceded the new cases in the sub-cluster could push out the outbreak's long tail by weeks, but that would depend on how quickly close contacts could be traced and isolated.
This morning, the ministry released a number of locations of interest, including Crave Cafe in Morningside which was visited by a Covid-positive person between 9.30am until 3pm on September 4.
Other locations of interest include Kreem Bake Cook, a cafe in Henderson, and Bricklane Restaurant and Bar in New Lynn.
The ministry said anyone who visited those places during the relevant timeframes was a casual contact with low risk of exposure.
They are not required to self-isolate unless they start to feel unwell or develop Covid-19 symptoms.
If they get sick, they are advised to call Healthline and stay home.
But close contacts have been told to isolate for 14 days, even if they test negative.