The Taoiseach has said that he looks forward to engaging with new Conservative Party leader Boris Johnson on Brexit, Northern Ireland and bilateral relations.
In a post on Twitter, Leo Varadkar congratulated the incoming British prime minister, and said that he looks forward to "early engagement" on the issues.
There is a sense of cordiality towards Mr Johnson in Government Buildings, but the mood remains resolute on the Withdrawal Agreement, which cannot be reopened.
The European Union congratulated Mr Johnson but was firm that it would not heed his election promises of renegotiating Brexit.
The bloc's executive European Commission was willing to work with Mr Johnson, a spokeswoman said, but the limits were clear.
"We look forward to working constructively with PM Johnson when he takes office, to facilitate the ratification of the Withdrawal Agreement and achieve an orderly Brexit," said the EU's chief Brexit negotiator Michel Barnier.
"We are ready also to rework the agreed declaration on a new partnership," he added, referring to a political declaration that accompanies the legal Withdrawal Agreement.
US President Donald Trump congratulated Mr Johnson on his victory.
"Congratulations to Boris Johnson on becoming the new Prime Minister of the United Kingdom. He will be great!" Mr Trump tweeted.
Mr Trump has declared himself a big fan of Mr Johnson.
Last week he predicted Mr Johnson would fix what Mr Trump called the "disaster" that outgoing PM Theresa May had triggered in trying to lead Britain out of the European Union.
"He's a different kind of a guy, but they say I'm a different kind of a guy too. We get along well. I think we'll have a very good relationship," Mr Trump told reporters.
Additional Reporting Reuters, AFP