Three household members of a remand prisoner with Covid-19 have tested positive for the virus, Ministry of Health says.

Corrections told RNZ the man initially denied having any symptoms of Covid-19 when he arrived, but they were detected the following day. He tested positive on Sunday.

The ministry said in a statement that two of the three household members attend Mangatangi School on the Hauraki Plains. All three positive cases, and an accompanying adult caregiver, are being moved to a quarantine facility.

"At least one of the young people was symptomatic at school on Thursday. The school has been closed and parents have been contacted. Arrangements are being made for the students and their families to be tested," the ministry said.

The ministry said there are nine people in the household. Five others have tested negative and the ninth household member will be tested on Monday.

The prisoner was released on e-monitored bail from Mt Eden Prison on 8 September to a residence in Firth of Thames, the ministry said.

"Electronic monitoring shows he remained at the property from when he arrived on 8 September until he self-reported to Police at the East Coast Road boundary checkpoint at Waharau Regional Park. He was held in custody in a cell on his own until his court appearance in the Manukau District Court on Friday, 17 September."

A pop-up testing centre will be set up on Monday at the Wharekawa Marae in Whakatīwai. The Ministry of Health is encouraging locals with symptoms to get tested.

Director of Public Health Caroline McElnay said earlier on Sunday that man had been travelling with one other person before he was taken to the prison.

"He is understood to have been in the Firth of Thames area before he was taken into custody, this is within the Counties Manukau DHB area, and is under alert level 4 restrictions," she said.

Two new places of interest have been added to the Ministry of Health's tracing list in connection with the man, one in Mt Albert and one in Māngere. And the person he was travelling with is being tested on Sunday.

"Five corrections staff and six prisoners are close contacts of the man and are isolating."

After arriving at the prison, the man made a court appearance and shared a cell with another prisoner before the positive test result was returned.

The national vice-president of the Corrections Association, Paul Dennehy, said it's not surprising there was a case at the prison.

"It's affecting New Zealand as a whole. This whole prison is just a microcosm of New Zealand society.

"And as a union, we're just supportive of all our members at sites across the country during this whole pandemic."

Mt Eden prison PHOTO: RNZ / Diego Opatowski

At Sunday's media briefing, Prime Minister Jacinda Ardern said it was "extraordinarily rigorous protocols" that had led to the detection of the virus.

Prisons are treated as a high risk residential environment, she said. All incoming prisoners are treated the same "as any individual coming to our border", and tested for Covid-19 on arrival, then retested up to day 12.

New arrivals are kept in a separate area to other prisoners for 14 days, and all staff interacting with them wear full gowns safety glasses, gloves, and masks.

The man on remand at the prison is one of the three as-yet unlinked cases from 24 new community cases announced on Sunday.

However Ardern said as the man was "essentially on parole" his movements were "very well known".

McElnay confirmed a tentative link to another case was known, and staff were working on confirming that, so it could be formally counted as a linked case.

Both the man on remand who tested positive and his cell mate are now in a quarantined area within the prison. Both will be supervised by dedicated staff who are all fully vaccinated, wear full length PPE and will not be in contact with other prisoners, Ardern said.

The four police staff exposed to the man are also isolating, three had been fully vaccinated and one has had one dose.

"Those who had contact with him will be regularly tested," she said.

The prison's chief custodial officer Neil Beales said only essential staff have been on site since the man's arrival.

"Mt Eden Corrections Facility was our first prison to implement our smart-card proximity detection technology to assist with contact tracing.

"We have provided information to all of the prisoners impacted so they fully understand the controls we are putting in place for their health and safety. They will continue to have access to Health Services staff who will assist them with any questions or concerns."

Staff welfare provisions were also in place, he said.

Ardern said prisoners were among Group 2 for vaccinations, because they lived in a residential environment.

"Auckland inmates have been among the first amongst inmates to be vaccinated."

Of the national prison population, 67 percent have had at least one dose.

Beales said vaccinations weren't compulsory for Corrections staff or prisoners.

"Since the launch of our vaccination programme in May we have taken a proactive approach to strongly encourage everyone to be vaccinated against Covid-19."