There appeared to be no repeat of the initial, heated phone call between the polarising Trump and Australian Prime Minister Malcolm Turnbull, during which they clashed over a refugee deal.
"It was a warm conversation," Ardern said.
"Regardless of the different views when they take on political issues, I will always advocate on New Zealand's behalf and that means a close and warm relationship with the United States."
Ardern, 37, had a longer Skype conversation with Canadian Prime Minister Trudeau on Tuesday.
Prime Minister Jacinda Ardern takes a video call from Canadian Prime Minister Justin Trudeau.
Like Ardern, Trudeau, 45, is the second-youngest leader in his country's history.
They spoke about being leaders when you are "slightly in a different age cohort than some of our counterparts" and also Apec, the East Asia Forum and challenges around trade agreements, Ardern said.
Trudeau tweeted he was "eager to meet in person soon to keep building ties and trade between our countries".
Skype chat with New Zealand PM-designate @jacindaardern! Eager to meet in person soon to keep building ties & trade between our countries. pic.twitter.com/3THoClAqXv
