Auckland Mayor Phil Goff says people in the city are, by and large, following the rules and prosecution shouldn't be ruled out for those who break them or spread misinformation.
Cabinet meets on Monday to review Covid-19 alert levels in Auckland and the rest of the country.
By then, New Zealand's largest city will have operated for two weeks at level 2.5 and it will have been over a month since restrictions were reintroduced to curtail community transmission.
The prospect of a lower level in Auckland may have been damaged by ongoing issues trying to contain the Mt Roskill sub-cluster.
Goff said they should only move to level 2 properly if it's safe to do so. He says the move down from level 3 was more important to Auckland than the next step.
"The big change for us was getting out of level 3. It was hugely welcomed and people have responded pretty responsibly to it.
"That opened up a whole range of businesses and brought back a lot of normality."
He said he's impressed to see Aucklanders take up mask wearing not just on public transport, but in public spaces including supermarkets.
Goff said it's a worry that misinformation is spreading but, by and large, people are doing the right thing.
"It is really obnoxious that people can spread misinformation, inaccurate information, lies, that can damage people's wellbeing and health through social media.
"There are fringe groups in any society, we've just got to make sure they remain fringe groups."
Goff said it's disappointing that members of the Mt Roskill church were sceptical about Covid-19 and held a meeting while level 3 restrictions were in place.
"We've all signed up for the rules."
He said prosecution is at the end of the line, but shouldn't be ruled out for people who knowingly break the rules or spread misinformation.
"The huge responsibility is the leader of fringe political parties going out and organising rallies and telling people there's nothing to worry about. That's what the President of the United States was saying too, so it's not limited to a fringe group in New Zealand."
Goff said it's not a failing of the government or health authorities to reach people who are sceptical, it's a failing of their own intellect.
"Anyone that goes out and says there's no such thing as Covid is just denying reality."