"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 Trump eventually realised who Ardern was, and that Ardern had also said that Trump was "not as orange in real life".
In a statement, Ardern said: "Someone thought the President had confused us, but in all of the conversations we had it was clear to me he hadn't, and recalled the conversation we had late last month."
Trudeau introduced Ardern to Trump in Vietnam while the three of them were standing in a small circle of leaders, all wearing their Apec silk shirts.
Ardern said she exchanged pleasantries with the US president and shook his hand, but did not have a substantive conversation.
Ardern and Trudeau were among the youngest and most liberal leaders at Apec.
A few days later in Manila, in the Philippines, they had a bilateral meeting on the sidelines of the East Asia Summit, in which she invited him to visit New Zealand.
Trudeau was one of the first world leaders to call Ardern after she became Prime Minister-designate, with Trudeau's office releasing a photo of him video-calling Ardern with an enthusiastic wave. Ardern's office also released a photo of the Skype call.
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.