Papatoetoe High School says it is willing to "pay the price" of staying closed until Monday so the rest of the country can move to less restricted Covid-19 alert levels.

Director-general of health Dr Ashley Bloomfield confirmed today three members of a second household connected with the high school have been found to have coronavirus, in addition to the first student and her parents who tested positive last weekend.

The new cases are a Year 9 classmate of the first case, the classmate's brother - who is in Year 12 at the same school - and one other member of their household.

The other two people in their household tested negative.

He said the two new students who tested positive for the virus, "Cases D and E", did not show any symptoms of illness when they were tested on Monday, and there was therefore a lower risk they might pass the virus on to others.

"Cases D and E were not at school during their infectious period," he said.

"However, to provide all possible reassurance, the high school will remain closed for the rest of this week and will reopen on Monday.

"All students and staff will be expected to have a negative test result before returning to school, and numbers have already done so."

School principal Vaughan Couillault said he has given all names on the school roll to the Ministry of Health and is waiting for the ministry to tell him which students have not been tested by Monday.

Asked whether he was happy with that arrangement, he said: "Hell, yeah, because the rest of the country is going down alert levels! If that's the price we pay to get the economy back and rolling again, hell, we'll pay it!"