During the 15-minute conversation, Trump and Varadkar, who were speaking for the first time, also delved into topics like Brexit and climate change (let's hope he convinced Trump of its existence).
Trump invites Ireland's new leader to WH for St. A small group of journalists was allowed to witness the start of the talks - an unusual allowance by the White House.
Varadkar, 38, is Ireland's youngest prime minister.
This is published unedited from the PTI feed.
"Congratulations on your great victory", Trump said to the Taoiseach. I know so many of them, I feel I know all of them.
"I just want to congratulate you".
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During an "introductory" phonecall this evening, Mr Trump said he looked forward to meeting the new Taoiseach in Washington next March.
Other topics discussed included migration, Brexit, climate change, free trade, Irish inward investment in the United States, and the undocumented Irish. Reporters were brought to the Oval Office for the beginning of Tuesday's conversation.
"I will not, of course, rescind that invitation".
According to a note of the conversation, they agreed to continue strong co-operation between Ireland and the USA on economic issues as well as shared cultural and family ties.
Mr. Varadkar said that he will raise issues such as climate change, LGBT rights, and immigrant rights on a future USA visit.
They discussed the supply and confidence agreement between the Conservatives and the DUP as well.
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