The Labour Party's Finance Spokesperson and Dublin West TD, Joan Burton, has officially declared she will not run for leadership of the party.
However Ms Burton has said she will run for the deputy leadership of the Labour Party.
Speaking on RTÉ Radio's Today show with Pat Kenny, Ms Burton officially ruled herself out of the leadership contest, saying she recognised that she does not have sufficient support to continue with that bid.
Instead she said she had spoken to party members across the country and there was good party support for her to run as deputy leader.
Limerick East TD Jan O'Sullivan and Cork South-Central TD Ciarán Lynch are both also seeking the deputy leadership.
Meanwhile, the acting leader of the party, Liz McManus, has said she will not announce whether she is contesting the leadership until after the party's National Executive Committee meets on Saturday.
Earlier this week, Brendan Howlin ruled himself out of the leadership race, which leaves Eamon Gilmore as the only official candidate so far.