Luxon says he does not agree with the comments, and he is calling on all political leaders to tone down similar inflammatory language.
Peters in his State of the Nation speech on Sunday said without NZ First in Parliament after the 2020 election, race-based theories had emerged.
"I've seen that sort of philosophy before. I saw it in Nazi Germany. We all did. We've seen it elsewhere around the world in the horrors of history," Peters said.
One iwi leader - Ngāti Kahungunu chairperson Bayden Barber said the speech played to Peters' voter base and the comparison was "pōrangi", or crazy.
Barber said his own grandfather was in the 28th Māori Battalion and fought against Nazism.
"We fought for the queen, for the king, and did so in a way to uphold the freedoms in Aotearoa. And so comparing Māori at the table, at the decision-making table, to participate in our future - which is what is espoused the Tiriti o Waitangi - is pōrangi rawa atu."
Labour leader Chris Hipkins said it was the "same old Winston Peters, using racism and anti-media rhetoric to divide our country".
"I ruled out working with Winston Peters before the election. Every day that goes by I feel more and more vindicated by that decision. Kiwis deserve better than a deputy prime minister who behaves like a drunk uncle at a wedding," he said.
Peters on Monday told Morning Report he was not backing down "one iota".
He responded to Hipkins with a tweet:
"Newsflash Chris. I publicly ruled out working with you and your woke Labour cronies twelve months before you stuttered the words. But you know that. And so do the media who have the temerity to repeat your stutter. PS. Your 'drunk uncle' comment is laughable coming from someone who would get drunk on a wine biscuit. Keep the press releases coming."
Speaking at his weekly post-Cabinet media briefing on Monday afternoon, Luxon said he has not had a chance to speak to Peters about the speech.
"No, I haven't had a chance to do so but we talk regularly and I plan to talk to him about it," he said. "Just from my point of view, that's not what I would say. I don't think that is... those aren't the way that I would phrase it at all."
He said he did not agree with the comments.
"I don't agree with those comments, that's not something that I would express."
However, he pointed also to comments by other political leaders.
"I just think in general across the politics and across the parties, across the aisle, there's a need for everyone to be careful with their language.
"I've seen Chris Hipkins refer to our government as a dictatorship, I've seen the Māori Party refer to us as white supremacists who have got some sort of genocide agenda. I don't think any of that inflammatory language is helpful at all."
He did not answer directly, however, when asked if it was problematic for his foreign minister to be using that kind of language.
"Look, again, all I can say is they're not the words that I would have used - but equally I see political leaders across the whole of Parliament that I don't think is very helpful, is inflammatory, and doesn't maintain the civility in our politics."
Asked if Peters would be sacked if he had been a National Party minister, Luxon only said: "Winston Peters and I talk a lot and regularly. We haven't had a chance to catch up today, but we will at some point, and we'll talk about it".
Hipkins at Parliament earlier defended his comments about the government, and argued he had not called Luxon a dictator.
"I said the government is behaving in a dictatorial fashion ... the point that I made last week is absolutely valid.
"When the government behaves in a way that suggests that they're not accountable to anybody, where they circumvent all of the democratic processes that we have by pushing laws through under urgency - including law changes that they did not campaign on, in fact, they campaigned on the opposite of what they have now been doing - I think that is behaviour that we should call out."
He said he stood by his statement about Peters, who should "start behaving like the deputy prime minister".
"I think the sorts of comments that he is making unnecessarily inflammatory and I don't think that he's living up to the standards of behaviour that we would expect from someone in that role ... I don't believe that his conduct is appropriate for someone holding their level of office that he currently holds.
"I will concede right now that Winston Peters tolerance for alcohol will be a lot higher than mine, he's had a lot more practice."
He said the sorts of comments Peters had made were racist and certainly seeking to stoke racism - and while it was appropriate for Peters as the Foreign Minister to be meeting with his Chinese counterpart today, "the unfortunate reality is that Winston Peters has a lot of baggage, and whether he can do so credibly really is a question for the current government".
That referred to some of the comments Peters had made about immigration in the past, Hipkins said.
"He is our foreign minister and our deputy prime minister and so when he makes comments about the Holocaust, when he makes comments attacking our migrant communities, they are seen as the position of the New Zealand government."
He would not be "commenting on every rant and rave of Winston Peters, but I do think the prime minister needs to accept that Winston Peters' overall conduct isn't really living up to the office that he holds".
Hipkins said Luxon should haul Peters in "and say, 'Stop this, this isn't acceptable'".
Luxon has only promised to speak to Peters, but his own rhetoric makes a change from when he defended Peters for attacking the media shortly after the coalition was formed.
At that time, he said Peters' comments were "fine" and "acceptable" and "being able to build within a team of a diverse range of views, a diverse range of personalities, is a good thing".
