The Taoiseach says there are too many serious issues in play for him to consider stepping down, just yet.
Speaking in New York he said he can't leave until a new government has been appointed in Northern Ireland.
He also wants to stay until the terms of reference for Brexit talks are agreed.
That's expected to take two months once Article 50 is triggered.
Before travelling to the US Enda Kenny told the Fine Gael parliamentary party that he would deal with the leadership issue after the St Patrick's Day trip.
Political Editor with the Irish Times Pat Leahy says he could be given some room for manoeuvre :