The interaction was "bizarre", as the US bureau chief for Ireland's RTÉ News, Caitriona Perry, later described it on Twitter.
While speaking with Ireland’s new Prime Minister Leo Varadkar, Mr Trump singled out Ms Perry and signalled her to approach his desk.
“Come here, come here. Where are you from? We have all of this beautiful Irish press.
“She has a nice smile on her face, so I bet she treats you well," the US president said to Mr Varadkar.
The video of the interaction, Ms Perry posted to her account, prompted some to describe Mr Trump as a “creeper” and others to say women journalists should be treated with professional respect.
Hundreds of women’s marches took place in the days after Mr Trump was sworn in as president, holding up signs saying 'women’s rights are human rights'.
“Nobody has more respect for women than I do,” Mr Trump responded to Democrat candidate Hillary Clinton saying he belittles women during the final presidential debate.
