He told the Fine Gael Parliamentary Party he had two priorities, Northern Ireland and the need for certainty
The Taoiseach Enda Kenny said the issue of his leadership will be dealt with after the European Council summit on April 29th.
Mr Kenny told the Fine Gael Parliamentary Party meeting this evening that he wanted to stay in place to begin the Brexit negotiations.
Some sources now believe that a leadership contest will be triggered in the first week in May.
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 the media 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.
It follows Minister for Finance Michael Noonan stating that Mr Kenny should stay on for the second phase of the Brexit negotiations at the end of May or early June.