After scenes of crowded parks and public areas in Auckland over the weekend, Police Assistant Commissioner Richard Chambers has told Checkpoint 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.