Taoiseach Enda Kenny has said he will deal with the leadership issue after the EU Council meeting on 29 April. .
He told the Fine Gael Parliamentary Party he had two priorities, Northern Ireland and the need for certainty.
Mr Kenny also told the party that he wanted to leave strong foundations at the commencement of the Brexit negotiations.
Mr Kenny said he knows what he wants to do with regard to the leadership and there will be an orderly transition.
He said there will not be a vacuum.
He also got a round of applause at the beginning of the meeting for his speech on immigrants in Washington which has received millions of hits online.
Earlier, Minister for Foreign Affairs Charlie Flanagan said if the Taoiseach walks away from his position on the eve of the Brexit negotiations it would be greeted with shock among his EU colleagues, who he said value his expertise and experience.
Charlie Flanagan told RTÉ News that for Enda Kenny to quit now is hardly the best option.
The negotiations, he said, present huge challenges on a number of key issues.
He is the second minister in recent days to suggest Mr Kenny should be present for key Brexit negotiations.
Minister for Finance Michael Noonan has already stated his view that Mr Kenny should stay on for the second phase of the Brexit negotiations at the end of May or early June.
Yesterday Mr Kenny told the Dáil that he intends to still be in office when he attends the European Council meeting at the end of next month.
The Fine Gael Parliamentary party is to meet this evening, but it is unclear if Mr Kenny will address the leadership issue as he had previously said he would on his return from America.
Since meeting US President Donald Trump, Mr Kenny indicated that Northern Ireland and Brexit are his priorities, which took precedence over all other issues.
The two leading contenders to succeed Mr Kenny, ministers Leo Varadkar and Simon Coveney, have both said those comments did not indicate any significant change.