Two Auckland bars were shut down by police overnight after refusing to follow level 2 rules.

Bars and other establishments that exist mainly to serve drinks were allowed to open from Thursday, but strict rules are in force to stop the spread of Covid-19 and businesses that break them have been warned they could be closed.

The two errant bars were in Auckland's CBD and Counties Manukau, police said in a statement. It's not clear what rules they broke.

A police spokeswoman declined to name the bars, citing privacy.

Police assistant commissioner Scott Fraser said the two premises "did not respond to education or encouragement to comply" with the restrictions.

"As such, those premises were shut down for the night."

Like at restaurants and cafes - which were allowed to open 10 days earlier - strict rules are in force at bars under alert level 2.

They include only allowing groups of 10 or fewer kept at least one metre apart, seated service only, and a single server for each group.

Patrons' details must be recorded for contact tracing and no more than 100 people - apart from staff - are allowed in at one time.

It's been suggested the rules mean some bars and clubs will be unable to operate profitably under level 2 and are unlikely to reopen yet.

Fraser said otherwise police had been generally pleased with the behaviour of people at licensed premises over the weekend.

"Establishments have also largely been receptive to advice and education given in relation to Covid-19 alert level 2 restrictions."

Police would continue to focus on educating people and businesses, carrying out reassurance patrols and visiting businesses and licenses premises, he said.

"Serious or persistent" breaches could result in enforcement action.

On Monday morning Cabinet will meet to consider whether the maximum number of people at gatherings can be raised under level 2, with an announcement to be made later tomorrow.

If a decision is made to increase the 10-person cap, it could come into force within 48 hours.

Prime Minister Jacinda Ardern said last week she had "huge faith" that bars would stick to the "three S" rules - seated, separated, and single service.

Ardern acknowledged times have been tough for owners and bar staff and she wished them well.Ardern has signalled that while alert level 1 is likely to be a long way off, the restrictions in place in level 2 could be gradually eased.