The prime minister sat down with his soon-to-be deputy, David Seymour, on Monday night after the two exchanged barbs over whether the ACT leader's conduct had been "ill-advised".
On Monday, Christopher Luxon called Seymour's letter to police in defence of Philip Polkinghorne "ill-advised" given an investigation was underway.
Seymour responded by going on RNZ's Checkpoint and doubling down.
He threw the criticism back at the prime minister, saying Luxon was the one out of line.
"What's ill-advised is commenting when you don't know all the facts and criticising a local MP for doing their work, which is standing up for their constituents."
On Tuesday, following a conversation with Seymour - who will take over as deputy prime minister in May - Luxon summed up his meeting as good and constructive.
"Look, I have confidence in David Seymour, he's doing a great job as associate minister of education, making sure we get our kids back to school.
"We had a good conversation last night, a constructive one as we often do, and we're a government that's got to be focused on economic growth."
Luxon added that he did not spend much time thinking about Seymour.
Seymour said there was nothing to patch up in last night's meeting as his relationship with Luxon was strong and constructive.
"[Our relationship is] very strong, very constructive and really our opposition's worst nightmare.
"Much as they'd love us to be divided, we've actually delivering a very good policy programme around improving the economy and I'm really proud of my contribution to that."
He would not be drawn on specifics of the discussion, including what was communicated about the Polkinghorne letter, but said the pair were allowed to publicly disagree.
"I don't think we need to patch it up, our relationship is strong, but I just correct one thing.
"We both called someone's actions ill-advised, in his case my writing of a letter and in my case his description of that action but at the end of the day you can still have a very strong relationship with a person without neccessarily agreeing with everything they say."
Finance Minister Nicola Willis however took aim at Seymour, who was also in hot water with Parliament security and the speaker on Monday for driving a landrover up the stairs of Parliament.
Willis said she did not spend her time "worrying about other politician's stunts".
"We're all here to serve the people, and not just ourselves."
She said Cabinet was a "functional" environment and her own relationship with Seymour, one of her associates, was constructive.
Another senior National minister, Chris Bishop, told RNZ the "disagreement" between Seymour and Luxon was just part of a robust democracy.
Chris Bishop. Photo: RNZ / Marika Khabazi
"We live in an MMP environment. Political parties who make up the government have different views, that's always been the case. It was the case under the last Labour government, it's the case under this government, it was the case under the last National-led government before that.
"We live in MMP, parties are not monochromatic institutions that all agree all the time."
He noted he would not have sent the letter on Polkinghorne's behalf, echoing Luxon's view that it was "ill-advised".
"I think that's pretty clear for all to see."
Police Minister Mark Mitchell warned there was a careful line for MPs when getting involved in court cases on behalf of constituents.
"You've got to be very careful that MPs - they have an important role, there's no doubt about that, they can be a conduit - they've got to be very careful they don't actually cross the line where they start then trying to influence or interfere in an ongoing police investigation."
Mitchell told reporters Luxon and Seymour had a "strong, stable, working relationship".
Commenting on reports that the National Party was happy to see the electorate of Epsom - which Seymour is the MP for - abolished in any change in an upcoming Electoral Commision review, Luxon said that was for the party to respond to.
"The party wing are the people involved in those conversations. There's a process, an independent process that determines the electorates."
Meanwhile, the Labour leader said the prime minister had lost control of his future deputy.
Chris Hipkins. Photo: RNZ/Samuel Rillstone
On Monday Chris Hipkins called for Seymour to be sacked, and on Tuesday he said the two taking potshots at each other showed the government was at war with itself.
"It's clear that Christopher Luxon's own ministers don't have any respect for his position as prime minister - why should New Zealanders?"
In addition to the coalition dynamics at play, the prime minister is dealing with two polls showing the centre-left bloc could govern if an election was held now.
Luxon would not respond to questions about whether the headlines being generated by his ACT coalition partner were partly to blame for the government's poor polling.
He told RNZ he did not need to calm his caucus colleagues who might be concerned with the polling, because "we have a great united caucus and we're in good shape".
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