Prime Minister Jacinda Ardern says that the case of mistaken identity where someone had thought that Donald Trump mistook her for Justin Trudeau's wife has nothing to do with the Canadian Prime Minister.

On Sunday comedian Tom Sainsbury said Ardern had divulged some information to him about her meeting with Donald Trump last week while they were at Apec in Vietnam.

"I don't know if I should be saying this, but she said that Donald Trump was confused for a good amount of time thinking that she was Justin Trudeau's wife," Sainsbury said during a segment on Radio LIVE.

This morning The Spinoff cited an anonymous source saying that Trump had also said to Trudeau: "You've done well for yourself."

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Ardern said on TVNZ's Breakfast this morning that someone had thought that Trump had made the mistake, but she did not have that impression with her own interactions with Trump.​

"I'm in a circle. I'm with someone else. I didn't hear the full conversation. They observed what they believed to have been mistaken identity. I didn't pick that up. I then had an interaction that suggested he knew who I was. That was the point at which I had been properly introduced."

She has said that Trudeau had introduced her to Trump while they were standing together in a circle that also included Mexican President ​Enrique Peña Nieto​.

This afternoon at her post-Cabinet press conference, Ardern said she had seen the media reports "and not all of them are inaccurate".

Asked about Trudeau's involvement, she said: "It's got nothing to do with him as far as I'm concerned. And it's not a significant issue. I don't intend to go into any further detail on that yarn."

She added that she did not think any embarrassment had been caused.

Earlier on Breakfast, she said she did not want to cause a "diplomatic incident" and admitted she "should never have recounted the story".

After Apec, Ardern exchanged some light-hearted comments with Trump while waiting for a gala dinner at the East Asia Summit.

She said that Trump had "patted the person next to him on the shoulder, pointed at me and said, 'This lady caused a lot of upset in her country', talking about the election".

"I said, 'Well, you know, only maybe 40 per cent', then he said it again.

"I said, 'You know', laughing, 'no one marched when I was elected'. It was only afterwards that I reflect that it could have been taken in a very particular way - he did not seem offended."

Ardern took part in a women's rights march in Auckland that coincided with the millions-strong march across the US and around the world the day after Trump's inauguration in January.

The march took place six weeks before Ardern was elected the party's deputy leader and six months before she took over the Labour leadership.