NT Police Commissioner Jamie Chalker is urging people across the Top End to "do the right thing" but warns officers will hand out hefty fines to those who flout the rules.
Today is the first full day of a 72-hour snap lockdown in the Greater Darwin and Katherine regions.
Commissioner Chalker reminded people it was mandatory to wear a mask if they left home.
"If you're truly committed to the Northern Territory, and want to help us out, just do the right thing," he said.
Commissioner Chalker said four people had been fined $5,000 each for not wearing a mask while allegedly breaking into a Darwin restaurant.
"That's over $20,000 for those four people that are breaking into a business that already has been impacted by lockdown," he said.
"Please do not target businesses who are already under the pump because of the lockdowns."
Commissioner Chalker warned other would-be offenders that police would add a $5,000 fine on top of all criminal charges if they could prove they were not wearing a mask at the time of the incident.
Supermarkets to remain open during lockdowns
Commissioner Chalker also voiced disappointment with people crowding shopping centres in Darwin and Katherine.
"We don't need to surge the supermarkets, they're still open," he said.
"When we're going into a lockdown, the intent is for you not to associate with as many people as possible.
"So please, for any future lockdown developments have sufficient supplies on hand."
He said only one person from each household should visit the shop at any given time and they should do so as quickly as possible.
As this was Katherine's first lockdown, Commissioner Chalker said authorities would take an education-first approach.
"But for people in Darwin and the Greater Darwin area this is not your first dance, you've been through this before you know what's expected," he said.
He said NT Police had received several calls about stories that were still trading and "probably pushing the boundaries as it relates to being essential" and officers would today be visiting businesses.
Keep checking in to businesses
NT Chief Minister Michael Gunner urged everyone to keep checking into businesses, right across the Territory.
"Compliance has been good, but it has not been great," he said.
"It needs to be great, check in every bloody time, check in, check in.
"There's absolutely no excuse whatsoever for not doing it is the easiest thing in the world take your phone out your pocket to scan the barcode."
In the NT, there are 2,098 people in quarantine and 43,793 compliance checks have been carried out.
Altogether, 321,815 COVID-19 tests have been conducted and there are three active cases in the Northern Territory.