There have been 104 breaches of alert level 3 so far and Prime Minister Jacinda Ardern has grilled one Kiwi fast-food chain for failing to keep customers physically distant.
Twenty-one people have been prosecuted, 71 warnings issued, and 742 complaints were laid about businesses flouting the rules, mainly about a lack of physical distancing.
Ardern said she had seen photos of people congregating, and Government officials had reached out to businesses to help them stop such congregations.
The rules of alert level 3 would be enforced, she said.
Ardern said she had seen photos of people congregating at a BurgerFuel outlet in Auckland.
"We have had confirmation from officials this morning they have been directly in contact with the head office of that operation."
She said the Auckland BurgerFuel outlet was clearly failing to keep people physically distant last night.
Director general of health Ashley Bloomfield said the overall message was still the same: "Stay home, save lives."
There had been large groups of people congregating outside businesses, and he asked those businesses to consider how to maintain physical distancing.
Non-compliant premises can still be closed, he said.
Two new cases today
Bloomfield revealed there were two new cases of Covid-19 today, made up of one confirmed case and one probable case.
One of the them had arrived from overseas and was quarantined at the border, while the other was linked to an existing case.
It is the eleventh day in a row where case numbers have been in single digits.
A previous probable case has also been confirmed, Bloomfield said.
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The total of confirmed cases is 1126 and probable cases is 348, totalling 1474 cases.
There are no additional deaths to report.
There are six people in hospital, none of whom are in ICU.
Ardern said more Covid-19 cases would still pop up, and the clusters in New Zealand showed how easy it was for one case to balloon into dozens more.
She said the fact that New Zealand was in such a good position and appeared to have Covid-19 contained was evidence that the pandemic plan was not ill-prepared.
Auckland University Professor Des Gorman this morning told the Epidemic Response Committee that New Zealand should have put strict border measures in place in mid-February, but the inability to do so was a sign of how profoundly under-prepared we were and New Zealand was essentially caught "with our pants down".
Shutting NZ's borders
, Ardern said it was not tolerable to prevent New Zealanders from coming home.
She added that it would have been an "extraordinary" move to strand Kiwis overseas in overseas countries where their mere presence may have been illegal.
Bloomfield said the ministry's advice was based on a public health perspective, which considered it "ideal" to close the border to all people.
It was based on advice on the need to close the border before a secure system to quarantine people was in place.
But he added that such a system was put in place quickly.
"We've been successful. Cabinet's decision was made with the expectation that we manage the risks at the border," Bloomfield said.
Ardern said Cabinet considered the ministry's advice before the level 4 lockdown.
The quarantine system was now proving its worth, she said, with about 25 people testing positive for Covid-19 while being isolated.
Health Minister moves house
Ardern was asked about Health Minister David Clark and reports that he had been moving house during the lockdown.
Clark has said that he was using his old house as a workplace, and had walked boxes to his new house which was on the same road as his old house.
Ardern said Clark, who has already been criticised for breaking the lockdown rules by driving his family to the beach, had not broken the rules in this instance.
"I will not hesitate to act when it comes to a minister who I believe warrants an action against them," Ardern said.
"In this case I do not believe that is the case, based on what I've been advised."
1 per cent of kids head into school
She said there were 7713 children showed up to ECE centres this morning, or 4 per cent attendance, while 11,846 students showed up to school, or 1 per cent attendance.
That showed that New Zealanders were taking level 3 seriously and parents were keeping children at home where possible.
Ardern said Cabinet was considering further help it could offer to businesses to pay commercial rents.
In a statement, Justice Minister Andrew Little said changes to the Property Law Act could support businesses in managing their rent.
"This includes how parties to a commercial lease would be expected to consider rent concessions in whole or in part for a period where the response to Covid-19 has had a material impact on a business.
"The lockdown has affected businesses in different ways and it wouldn't be fair to have one solution - like a rent freeze - for every situation, especially when in many situations landlords have already agreed to rent reductions.
"Landlords need to share the burden of Covid-19 fairly with their tenants."
He said commercial rent freezes would mean commercial property owners would have their income protected at a time when no one else enjoyed the same privilege.
Asked about people arriving from overseas to visit a Covid-afflicted person in New Zealand, Bloomfield said such people can be granted an exemption from mandatory quarantine, but those were granted in very limited circumstances.
"I will make sure the process is expeditious and fair," he said.
Bloomfield yesterday clarified that elimination did not mean zero cases, and it was an ongoing mission that required ongoing vigilance from everyone.
He told Newstalk ZB's Mike Hosking this morning that he did not believe he had "got ourselves into a pickle" over the use of the word elimination.
"I think we got ourselves out of a pickle with where coronavirus was heading."
He said the World Health Organisation had praised New Zealand's efforts, but that also came with a warning "not to take the foot off the pedal".
Elimination, he said, was not a point in time but a sustained effort - to keep Covid out of the country and to stamp it out as cases arose. "It's like killing weeds on your lawn, you can kill them all but they sure as heck will pop up again."
He shared the PM's aspiration to get down to level 2 as quickly as possible - that would depend on Kiwis' behaviour over the next two weeks, especially in regards to physical distancing. "That's going to be the big one."
The number of New Zealand cases might increase, Bloomfield acknowledged.
"Critical is knowing where they have come from. If it's from a known source, that's much more comfortable than if they are popping up out of nowhere."
There was a huge international effort under way to develop a vaccine, with more than 100 trials.
Despite New Zealand effectively eliminating Covid, Ardern warned the fight wouldn't be over until there was a vaccine.
Elimination did not mean a point in time, instead would be a sustained effort to stamp out every new case, she said.