Fianna Fáil TD Marc MacSharry is calling on Taoiseach Micheál Martin to resign as party leader this summer.
It follows its poor performance in the Dublin Bay South by-election, where it got less than 5 per cent.
Another party deputy, Barry Cowen, is calling for a special meeting to address the 'alarming' showing.
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Deputy MacSharry says Mr Martin should stand down during the Dáil's summer recess.