The Taoiseach also held a call with the UK Prime Minister, Theresa May, this afternoon in which they discussed the ongoing efforts to restore the Executive in Northern Ireland ahead of Thursday's deadline, and the supply and confidence agreement between the Conservative Party and the DUP.
Mr Trump did however extend to the Taoiseach the traditional invite to the White House for the annual St Patrick's Day celebrations.
President Donald Trump, accompanied by National Security Adviser H.R. McMaster and National Economic Council Director Gary Cohn, talks with new Irish Prime Minister Leo Varadkar during a telephone call, Tuesday, June 27, 2017, in the Oval Office of the White House in Washington.
"Congratulations on your great victory. That was a great victory that you had", Trump said.
"I just want to congratulate you".
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He said he would not vote for any Liberal bill until the confidence of the house has been tested. This is an effort by this government to hold on to power for as long as they possibly can.
"Particular topics discussed included migration, Brexit and the movement of goods and citizens across the border, climate change, free trade, Irish inward investment in the United States, and the undocumented Irish", the statement said, as well as the Northern Irish peace process.
The Taoiseach said numerous illegal Irish in the USA had originally travelled on legitimate documentation but for a variety of reasons now needed to regularise their situation.
Tells the new Taoiseach that there were Irish press in the Oval Office for his photo op congratulatory phone call to him. "It would be inappropriate and create a diplomatic incident if I was to rescind an invitation once made but no progress has been made in organising such a visit, for which there is no timeline", he said.
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".
Mr. Varadkar will have his chance next March and before then if President Trump visits Ireland.