The two leading contenders to succeed Taoiseach Enda Kenny have insisted his comments to last night's parliamentary party meeting have settled the issue of when he might step down.

Minister for Housing Simon Coveney said Mr Kenny had spoken with authority and Minister for Social Protection Leo Varadkar said the party was relieved damaging divisions had been avoided.

Mr Kenny spoke for six or seven minutes from a few pages of notes.

He told his party he was committed to meeting Brexit and other challenges and that he was dedicated to avoiding any course of action that might damage the party or the country.

He said he intended to address the issue of his leadership shortly after his return from Washington for St Patrick's Day celebrations next month and would deal with it effectively and conclusively.

Those present said he spoke with seriousness and authority and drew applause from the 70 or so present.

His remarks suggest he will trigger a leadership contest in late March that would see a new party leader towards the end of April in time for the new Dáil session after Easter.

Mr Kenny’s speech has quelled his party critics who now trust him to stick to that timetable.

Speaking on RTÉ's Morning Ireland, Mr Varadkar said he was relieved that "we avoided acrimony, we avoided a motion of no confidence, we avoided the kind of negativity that I don’t think anyone who has politics as a career, as a job, really likes and we avoided all of that”.

He said some parliamentary party members were tense ahead of yesterday’s meeting and there was "a concern" the party "would be facing a showdown".

"Because of the way the Taoiseach handled the meeting that didn’t happen. So, we didn’t go back to the Fine Gael family at war that people would have known about from the past. In that sense, it went really well," Mr Varadkar said.

Mr Varadkar said the leadership campaign is not open and can only start when a vacancy arises, adding that he did not envisage any "overt or covert campaigning" between now and St Patrick's Day.