Canadian leader 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.
At the time, it was reported that it took the President several minutes to realise his mistake.
However, Ardern said she regretted the gossip getting out and played down the story after reporters seized on it.
She said she didn’t want to “cause a diplomatic incident” and claimed some details were mangled in the retelling.
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.
Then, she said that she would be more careful when gossiping about other world leaders, in case of more leaks.
“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.
This comes after she said she had a minor spat with Trump at a summit in Asia.
She said last week she met Donald Trump at the East Asia Summit gala dinner, when Donald Trump patted the person next to him on the shoulder and said “This lady caused a lot of upset in her country.”
She told the website that she smiled and replied “Well, you know, only maybe 40 per cent!”
Then, the President repeated his comment.
In return, she shot back: “You know, no one marched when I was elected.”
This appeared to refer to the fact many took to the streets to protest after Donald Trump’s unexpected election win.