Mr Trump pointed at RTE reporter Caitriona Perry and beckoned her to his desk in the Oval Office, telling Prime Minister Leo Varadkar: "She has a nice smile on her face."
The 71-year-old business mogul-turned-politician added: "So I bet she treats you well."
Mr Trump, who faced calls to withdraw from last year's presidential election over inappropriate remarks about women, was criticised on social media for the exchange, which Ms Perry described as "very bizarre".
In the call, Mr Trump told Mr Varadkar "We have a lot of your Irish press watching us right now" before singling out Ms Perry.
As he pointed at her and beckoned her with his index finger, the president added: "And where are you from? Go ahead, come here. We have all of this beautiful Irish press. Where are you from?"
After Ms Perry gave her name and organisation, Mr Trump said: "She has a nice smile on her face. So I bet she treats you well."
He added: "He thanks you for the newspapers, Caitriona."
Ms Perry, the Washington correspondent and US bureau chief for RTE, and a few others laughed as she returned to her spot in the room and the call continued.