Director-General of Health Dr Ashley Bloomfield says he has no explanation as to why Papatoetoe High School students refused to take a COVID-19 test.
All students and staff were required to isolate and undergo testing after the original case - a Papatoetoe High School student - was confirmed positive for the virus on February 14.
On Thursday, Dr Bloomfield said two people had refused to take a test and two others were unwilling to take a second test.
The Director-General says he has no understanding as to why tests are being refused.
"Look, I think we see this as well in managed isolation. It may be just a belief system," he said on Thursday.
"There is a small number of people who subscribe to a belief that COVID-19 doesn't actually exist. I know that the vast majority of people don't subscribe to that.
"Or it may just be they really, really do not want to have a test."
Dr Bloomfield reassures that the people who refused to take a test have chosen to isolate for a 14-day period, and are being monitored.
"If they did have COVID-19 and clearly, if they became symptomatic then that would become a different situation."
As of Thursday, 11 Papatoetoe High School students have not returned a second test.
Of those students, eight were visited by the MoH on Wednesday, and two refused to take tests but had isolation plans in place.
One student is being tracked down by the Ministry of Health but the student is known of and had previously returned a negative test.
There are no new cases of COVID-19 in the community on Thursday and six cases in MIQ facilities.
Although we haven't seen new cases since Saturday, COVID-19 Response Minister Chris Hipkins says New Zealand still remains in a "critical period".
"I think we're still in the critical period where we're wanting to see all the test results of the relevant close and casual contacts come back, so that work is still underway," Hipkins said on Wednesday.
"There's some test results still to come through for people who we really want to see the test results for before we can breathe any kind of sigh of relief."