The AI-generated video was among 70 messages Trump posted on Thursday night (US time).
It was later deleted, and the administration blamed a staffer after initially defending the post.
Speaking to TVNZ's Breakfast, Christopher Luxon said Trump should apologise.
"Yeah, look, I think he should," he said.
"I mean I think when he was asked I think he said he condemns it but the reality is I saw coverage of it, I lived in the US for eight years in North America, and I'm well aware of what that trope is all about.
"It was racist, and it's right that it's been removed. As to whether he apologises for it that's ultimately for him, but I would've thought you'd want to."
Some Republicans have joined Democrats in decrying the post and calling for an apology.
Trump has not yet apologised.
