The latest Covid-19 community case had contact with an infected family during alert level 3, the Prime Minister says.

Jacinda Ardern's comments come after it was revealed a recent case went to the gym when he should have been at home after having a Covid test - something that has angered many in the community and generated numerous calls for greater consequences for those who don't self-isolate.

Ardern says there is a confirmed link between the latest positive case and an earlier family.

Ardern told Newstalk ZB's Mike Hosking this means there was a direct chain of transmission in the current outbreak.

She said after a number of interviews, officials discovered the new contact.

The two families had contact under level 3, Ardern said.

"Obviously we've had contact here in level 3 when it shouldn't have happened," she said.

"This was a family who was already identified as having Covid and so was part of contact tracing and did not identify that they did have contact with this family," Ardern said.

"So that means we go back, we re-interview and say 'now that we have identified that this has happened, we haven't had all of your contacts, are there others?' and we do all we can to identify whether or not there's anyone else that there's been contact with."

"The most important thing to us is people just telling us. Obviously, we've had contact here in level 3 when it should not have happened but the best thing people can do is still tell us the truth," said Ardern.

"Had we known this, the other family that we've now found a week later, they would have been a close contact and they would have been in quarantine and we would not have had this situation. The truth is so important to us."

Ardern told The AM Show the person had been interviewed by officials and did not disclose the meet-up.

"Whether or not they forgot or lied, I cannot tell you and it's obviously had devastating consequences," she said.

She said whether or not any action would result was not up to her.

"People do dumb things but we're not going to get through this if people pillory them to the point they do not tell the truth."

She said there were multiple breaches that happened across two families at the centre of the outbreak.

"A decision on whether enforcement action happens or not is not mine," she said.

Ardern said she was constantly in two minds over saving people from dying and keeping people onside to follow rules.

"It's a difficult dilemma," said Ardern, who admitted she was angry.

She hoped the greatest deterrent was witnessing what was happening right now with the heightened level of public accountability.

She wanted people to be honest with health officials.

"We have been here before," she said, referring to people who were not compliant during Auckland's August outbreak.

The PM told Hosking that people in isolation were subject to daily checks by health officials and, for the most part, were following the rules.

She said there was no excuse for what happened.

Ardern is warning more community cases are likely to be discovered in coming days so it's important people follow lockdown rules because "Covid kills".

And she has a blunt message for anyone who is not complying with isolation rules – expect a knock at the door from police.

When people went to a GP for a test, staff made it very clear to stay home after they have a test, she said.

Of the long queues of motorists trying to get back into Auckland, Ardern said what we saw happen on the roads yesterday was the effect of a lockdown taking place in the middle of a weekend.

She said the Government did not want additional people in Auckland in a heightened alert setting.

Additional staff from defence have been drafted in to help ease queues.

"MBIE here have done an incredible job. Yes, the first level 3 was tough and we needed to improve at the border. Now we have a regime where everyone is just reissued their documents so they are able to move straight away," she said.

Meanwhile, as Auckland entered its first day at level-3 restrictions, there was chaos and confusion at several police road checkpoints at the region's borders. Some families were still trying to get home last night after spending 10 hours stuck in traffic at Auckland's Covid-19 checkpoints.

Aucklanders are back in level-3 restrictions for a full week and the rest of New Zealand is at level 2 after the 21-year-old MIT student - known as Case M - visited various public locations before testing positive.

He then went to the gym when he should have been in isolation. His mother, Case N, has also tested positive.

Last night, a new case - Case 0 - was revealed from the same household, while several new locations of interest were released into the movements of Case M, including an MIT cafe and Pak'nSave Cavendish Drive, as well as new times for Hunter Plaza and the City Fitness gym there.