Last Thursday, health authorities announced a security guard at New Zealand's biggest quarantine facility, the Grand Millennium hotel in Auckland, had contracted the virus.

By Monday, two further cases - a security worker and a cleaner - were unearthed, with genome sequencing showing links to the original case and a recent returnee at the facility.

Prime Minister Jacinda Ardern has downplayed the risk of an outbreak, saying the new cases had already isolated.

Ms Ardern told 1News she and the Director General of Health Ashley Bloomfield were "not anxious".

"It's someone we already identified, so that's always heartening," she said.

"As they are a close contact ... they were already in isolation."

While a small number of community cases previously prompted Australia to pause quarantine-free travel from New Zealand, on this occasion it has not done so.

Last week, Ms Ardern announced New Zealand would reciprocate quarantine-free travel from Australia from April 19, effectively creating a trans-Tasman bubble.

"That's a demonstration of the fact every case will have its own circumstances," Ms Ardern said.

"In this case, someone has been picked up in our surveillance, it's linked to a known case, locations of interest are small, (there has been) very good communication between our officials."

While the spread may have been contained, the new cases have brought to light concerns over New Zealand's vaccination program.

The government has prioritised all border workers and front-facing health professionals in the rollout but six weeks on, many have not been vaccinated.

Ms Ardern said 86 per cent of the 4010 quarantine-hotel workers had received at least one shot of the Pfizer vaccine.

Dr Bloomfield said two of the three recent cases had not received their shots.

"There is no suggestion they are vaccine hesitant," he said.

"Many people on the front line have been vaccinated and others are in the process of being vaccinated.

"It's a large workforce. Everyone has been invited. Some haven't yet taken up that invitation."

Ms Ardern has also defended a move to block Kiwi citizens travelling home from India.

Her government banned incoming travel from India last week in response to a spate of positive cases in New Zealand's managed isolation regime.

"Had we seen things happen from Brazil, from the United States, I would do the same thing," she said.

"We were looking for ways to reduce down the number of infections coming in.

"It is only a pause. We can not and will not permanently stop citizens from coming home. We're pausing to get this a little bit tighter than it is now."

Australian Associated Press