Cabinet meets on Tuesday and Deputy Prime Minister Winston Peters says alert level 2 restrictions have to be discussed.
Thousands collected across the country, including at Parliament, on Monday for Black Lives Matter marches where social distancing and mass gathering rules were flouted.
Peters said the breaching of alert level 2 rules at the protests should have resulted in prosecution for the organisers.
And 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?"
Peters 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."
Despite 10 days of no new COVID-19 cases Cabinet isn't due to review level 2 settings until Monday, June 8.
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," Peters said.
So will Cabinet discuss it on Tuesday?
"It would be very difficult if it's not a matter of discussion because of what's happened a day before Cabinet," Peters said.
The last day set down for Cabinet to consider easing restrictions is 22 June.
"It's not a matter of saying something new ... we've already had two cycles of 14 days, we will, in fact, be well past 30 days of no community transmission events. But the rules are the rules and until the decision is made to go from level 2 to level 1 then we expect people to comply with the rules."
He said that some people thought they were above the law was unacceptable.
What has happened at Monday's marches has to be responded to "and it will be", Peters said.