ACT Chief Minister Andrew Barr has warned businesses found to continuously ignore directions were at risk of being shut down.

"We are now moving beyond warnings," Mr Barr said. "Repeat offenders will have to be closed."

ACT Policing, Access Canberra and WorkSafe ACT conducted 37 business compliance checks on Sunday, as well as 376 traffic stops.

Mr Barr said the reports from the three separate areas of government was reason for concern.

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"The purpose of the public health directions is to protect the community and to protect the staff working in businesses," the Chief Minister said.

"If we can't, this far into the pandemic and this far into the lockdown, have compliance levels incredibly high we are beyond the point of issuing warnings."

It comes as ACT records another 13 new cases of COVID-19 in the 24 hours before 8pm on Sunday.

Overall, authorities have reported that Canberra residents have generally been well behaved when it comes to complying with health directions.

However, Mr Barr has repeatedly pointed out non compliance with business operators.

When pushed on the issue on Monday, the Chief Minister conceded it was mainly hospitality venues that continued to breach health directions.

The main problem was with staff improperly wearing masks, Mr Barr said.

Authorities had also reported non compliance during the click-and-collect process.

Mr Barr said while the ACT had always had an engage and educate starting point, authorities wouldn't hesitate to hand out fines or shut down the businesses that didn't heed the message.

"You might recall that at various points interstate you had police arresting people for eating kebabs in parks, and that sort of thing," Mr Barr said.

"We have never had that culture of a heavy handed police state in this jurisdiction, and I hope we never will, but what we do insist is that in order to keep everyone safe and to keep all the other businesses open and functioning is these public health directions are complied with."

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