The Taoiseach has said other EU leaders are very much aware of Irish interests in negotiating the UK's exit.
Enda Kenny has told a Dáil committee there was no hysteria or panic in Brussels in the past two days about Brexit.
And he said his counterparts know exactly what Ireland wants when Britain leaves: “The European Union is very aware of the common travel area that we have had with Britain since ’22.
“They are very much aware of the peace process. They are very much aware of the open border that we have with Northern Ireland.
“They are very much aware that our particular interests and our pivotal position now between the UK and the EU.”
Meanwhile, Irish property experts have said in the short term Dublin may benefit from Brexit - as international companies based in the UK relocate here - to stay within the single market.
Maria Hunt who is Head of Research with the commercial property firm CBRE expects a number of financial services, technology and other firms to move from Britain.
However she has said our overall property market will be hit by the general economic uncertainty caused by Brexit.
She said this may cause some investors to delay making decisions: “Anything that creates uncertainty is unwelcome in the property market be it residential or commercial.
“To say that the Brexit vote has created uncertainty is really an understatement.
“So I think it will be some time before we understand fully, implications for the economy and the real estate sector, but in the short term, I think that some decisions might be delayed.”