Trudeau was supposedly making the introductions as Ardern attended her first major forum since taking office last month when Trump mixed-up the 37-year-old with the Canadian leader's partner Sophie.
It was reportedly several minutes before he realised his mistake at the East Asia Summit in Manila.
However, Ardern said details of the encounter had become muddled in the retelling and there was actually no confusion on Trump's part.
She said "a third party" at the meeting of world leaders -- who she refused to name -- incorrectly thought Trump had failed to identify her and she later told the anecdote to friends back in New Zealand.
A version leaked publicly that was unflattering to Trump and the rookie prime minister said she would now have to be more careful when telling tales of her encounters in the corridors of power.
"It was a bit of a funny yarn, something I don't want to cause a diplomatic incident over... I think I should never have recounted the story," she told TVNZ.
It comes after Ardern recalled another Trump anecdote from the Manila summit, when she was waiting to make her entrance at the event's gala dinner.
"Trump in jest 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," she told newsroom.co.nz.
"I said, 'Well, you know, only maybe 40 percent', then he said it again and I said, 'You know', laughing, 'no-one marched when I was elected'."
Large protests followed Trump's election last year but Ardern said the American leader took her riposte in good humour.
"He laughed and it was only afterwards that I reflect that it could have been taken in a very particular way -- he did not seem offended," she said.
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