"We have a lot of your Irish press watching us right now," President Trump told Mr Varadkar. "We have all of this Irish, beautiful Irish press here."
He then singled out one journalist in particular.
"Where are you from," he asked the woman, motioning her to step forward. "Come here, come here."
The journalist in question was Caitriona Perry, the Washington correspondent for Irish state broadcaster RTE.
"She has a nice smile on her face so I bet she treats you well," President Trump told Mr Varadkar on the phone in front of journalists in the Oval Office. Ms Perry was shooting the scene on her mobile phone.
Ms Perry initially laughed off the incident. But soon after, she posted a short video to Twitter, terming it a "bizarre moment."
Retweeted over 7,000 times already, President Trump's comments have provoked strong reactions on social media.
Trump,"She has a nice smile on her face so I bet she treats you well."Ms.Perry, please accept the apology of at least 1 female American.— Christine Canning (@Canni2Canning) June 27, 2017
I am sorry our President treated you this way.— Jon (((Wolfsthal))) (@JBWolfsthal) June 28, 2017
Needless to say, male reporters are not told that they have a "nice smile" https://t.co/H8pH5CKZd7— Brendan Nyhan (@BrendanNyhan) June 28, 2017
It's hell to be objectified. When POTUS has no fear of doing that surrounded by cameras... I'm so sorry. Your success is more than a smile.— Cristin Harber (@CristinHarber) June 28, 2017
Here's the encounter from Ms Perry's point of view. This video was posted to Facebook by RTE.
(With inputs from AFP) Click for more trending news