Justice Minister Frances Fitzgerald has said that Enda Kenny has the full support of Fine Gael.
Minister Fitzgerald says Fine Gael would not go into negotiations to form a Government undermining their leader.
She said as the party has the largest number of seats, it is their responsibility to try and form a stable government.
Frances Fitzgerald has been tipped as a candidate to replace Enda Kenny, but insisted that the party is supporting him.
"The Taoiseach is the leader of Fine Gael, he has our support," she said.
"I mean, one does not go into negotiations undermining the leader of those negotiations, you go in supporting the leader who is involved in the negotiations, you give him the strongest support possible to put the case that we have, as the largest party.
"And that is the situation and we're not going beyond that."
Update 1pm: Speaking in Brussels, the Fine Gael leader said he doesn't think any candidate will have the necessary support to be elected as Taoiseach at the first meeting of the 32nd Dáil this Thursday.
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[/raw]Enda Kenny says he cannot 'put a date' on the formation of a new govt but a process is 'going on at the moment'https://t.co/DGtKTqYiKY
— RTÉ News (@rtenews) March 7, 2016
"Well, the indications are that nobody will be elected as Taoiseach on Thursday,” he said.
“You can never predict, in a situation like this, but clearly the fact of the matter is that the Taoiseach is elected by the Dáil and obviously continues until that situation is changed.
“For me, the work of Government goes on, that’s why I’m here today, that’s why I’ll be here again next week, if that be so, in respect to dealing with these serious issues.”