Police have not made any arrests for lockdown breaches since Auckland went back into alert level 3 last week.
They have issued four warnings reminding people of their obligations under level 3 though, a police spokesman said.
Two of those warnings related to gatherings, but there was no further information available on the nature of the gatherings, he said.
"Police have conducted thousands of reassurance patrols across essential facilities since last Wednesday. This includes supermarkets, pharmacies and Covid-19 testing sites."
Officers have been undertaking road policing activities, and patrols across essential facilities such as supermarkets, pharmacies, and Covid-19 testing sites.
"Our presence has also increased in the community."
At this stage no arrests have been made in regard to breaches of restrictions. However, four warnings around breaches have been issued in Auckland since the end of last weekend.
"Our focus remains on engaging, encouragement and education with the public." the spokesman said.
In one instance, police were sent to the St Heliers area shortly before 1pm on Sunday, where it was reported a number of people were failing to keep their distance from one another.
Officers showed up and spoke to people at the beach, who were all in their various bubbles and mainly there for exercise. They educated them on keeping their distance under level 3 restrictions.
The response was "largely positive", the spokesman said.
Police have been adding checkpoints around the Auckland region to stop people who are coming and going without good reason.
In a statement issued this afternoon, police said they had increased the number of checkpoints in South Auckland by three to eight.
The extra checkpoints come after motorists reported heavy delays south of Auckland.
Figures from last week showed more than 40,000 vehicles had been stopped at one of the checkpoints.
Just over 600 of those vehicles were turned around for what police described as "undertaking non-essential travel".
Police looking at issuing instant fines for rule breakers
After scenes of crowded parks and public areas in Auckland over the weekend, Police Assistant Commissioner Richard Chambers has told RNZ issuing fines could be a possibility.
He says police have issued warnings over alert level 3 breaches, but issuing fines is a bigger discussion.
"We are discussing those very points with Health and with All of Government group. There may well come a time when we need to take that approach."
But education is sufficient right now, and only a small number of rule breakers need warnings, he says.
"I think everyone understands what's expected and the vast majority of people are doing the right thing. There are a few who don't seem to understand or are ignoring those [rules] and, where we can, we have a conversation with them.
"We continue to say, please avoid unnecessary travel. The reason we're all doing this is for the greater good of all communities across Auckland and, ultimately, for our country."
Chambers said they were getting "fantastic support" from the community and people were making them aware of rule breakers.
"It's only a very small number we're having to warn," he said.
Chambers said they're now stopping motorists on all routes in and out of Auckland, including the back roads people have been trying to sneak down.
There are now 13 checkpoints operating to the north and south of the city, and more than 50,000 vehicles have been stopped so far.
Chambers told Checkpoint that people have now had time to get used to the rules, so more vehicles will be turned around in the coming days.
- Addtional reporting: RNZ