In their first telephone call since Mr Varadkar was appointed Taoiseach earlier this month, the pair did not discuss a visit to Ireland by the United States president.
Trump made the phone call behind his desk in the Oval Office, with press cameras and mics present of course.
During an "introductory" phonecall this evening, Mr Trump said he looked forward to meeting the new Taoiseach in Washington next March.
Before speaking with the Taoiseach, Mr Trump will also have a call with new French President Emmanuel Macron.
It remains unclear whether the U.S. leader's planned visit to Ireland will be discussed during the call. Trump said turning to Perry before the call according to a video posted by RTE.
Mr Varadkar's spokesman said the Taoiseach had held a number of phone calls with worldwide leaders since his appointment including Mr Macron, British Prime Minister Theresa May, German Chancellor Angela Merkel and Indian Prime Minister Narendra Modi.
Mr Trump also congratulated Mr Varadkar on his recent election as leader of the minority ruling Fine Gael party and his appointment as Taoiseach.
"I just want to congratulate you".
Added the taoiseach: "I assure the deputy that in any dealings I have with the American government and in the interactions and engagement I have with the chargé d'affaires who is here and who is acting US ambassador to Ireland, I will approach them based on the long-standing friendship that exists between our countries and the familial, cultural and economic links but I will never shirk from raising issues such as climate change".
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