Deputy Prime Minister Winston Peters says alert level 2 restrictions have to be discussed during today's Cabinet meeting.
Thousands gathered across the country, including at Parliament, yesterday for Black Lives Matter marches where social distancing and mass gathering rules were flouted.
Mr Peters said the breaching of Alert Level 2 rules at the protests should have resulted in prosecution for the organisers. If they won't be prosecuted, then there's no choice but to move to alert level 1, he said.
"If they condone that and there's no prosecution of the organisers of these two events then why are we not at alert level 1?"
The Deputy Prime Minister has already publicised his difference of opinion with his Cabinet colleagues over the speed at which the country was moving alert levels.
"Why is this going on against the rules we've all agreed to?"
"It's a question for all of us. We cannot have rules where some people decide that they don't wish to comply and there are no consequences," Mr Peters added.
Despite 10 days of no new Covid cases Cabinet isn't due to review level 2 settings until Monday 8 June.
But public and political pressure is mounting on Prime Minister Jacinda Ardern.
"The Cabinet agenda would not have envisaged such an event happening the day before Cabinet met, but we've got to go there with an open mind and understand that these matters have to be resolved and the law has to be upheld," Mr Peters said.
So will Cabinet discuss it today?
"It would be very difficult if it's not a matter of discussion because of what's happened a day before Cabinet," Mr Peters said.