A change of Prime Minister will not result in a change in the Irish Government's stance on Brexit, the Irish foreign affairs minister said.
Simon Coveney said the Government's position had not changed and will not change because of Theresa May leaving her role.
His comments came as some of the candidates in the Conservative party leadership campaign to replace Mrs May raised the prospect of a no-deal Brexit.
"The Government's position has not changed and it does not change because there is a change of British prime minister," Mr Coveney told the Irish parliament on Tuesday.
"This has never been about personalities. It has always been about evidence, facts and trying to deal with the complexity of the decision of a country and economy the size of the UK to leave the European Union, of which it has been a part for 47 years.
"The approximately 57 trade deals it has in place, the 70 billion euro trade relationship it has with Ireland, and the fact that we share responsibility for a peace process on this island, all make the UK's exit from the European Union very complicated.
"That is why the withdrawal agreement, which deals with that complexity in terms of the divorce arrangements for leaving, if one wishes to call it that, took two and a half years to negotiate.
"That is the EU's and Ireland's position and it is not going to change with a new person taking charge, regardless of what is being said and claimed.
He added that Ireland needed to be "respectful" in how it relays that to the UK, but the Government also needed to be "firm and consistent".
Meanwhile, the race forthe Tory leadership is hotting up with another candidate facing the axe on Wednesday following a TV debate which saw no clear winner.
Conservative MPs will decide which of the five remaining contenders – Boris Johnson, Jeremy Hunt, Michael Gove, Rory Stewart and Sajid Javid – deserves their support in a third elimination round.
The first debate involving front runner Mr Johnson on Tuesday night is unlikely to have swayed many MPs’ minds, ending with no clear winner after a fractious debate taking in Brexit.
The five candidates vying to become the next Prime Minister clashed over Brexit, including the future of the Irish border during a TV debate.
They offered differing visions of how a hard border could be avoided after Brexit.