The backbench Fianna Fáil TD Noel O'Flynn has called on Brian Cowen to resign as party leader, and for the Fianna Fáil Parliamentary Party to unite behind Minister for Foreign Affairs Micheál Martin.
Speaking to RTÉ News, Deputy O'Flynn - a TD for Cork North-Central - said he did not believe people had confidence in Mr Cowen and the party needed a new leader in order to win back public support.
He said he had been contacted by the Taoiseach by telephone late this afternoon as part of Mr Cowen's consultations with members of the Parliamentary Party, and he had expressed these views to him.
He said Mr Cowen listened to what he had to say and accepted that this was his position.
Deputy O'Flynn said Brian Cowen's leadership had not worked, while the revelations of the past week had not helped either.
He said he believed Mr Martin was the best person to lead the party into the General Election, to restore the confidence the party had lost and the support the party would need to win as many seats as possible in the election.
Mr O'Flynn said it was his understanding now - despite what Mr Cowen had told him at Thursday's Parliamentary Party meeting - that a number of ministers had gone to the Taoiseach in advance of that meeting and asked him to stand down.
He insisted that he was acting alone and had not contacted or been contacted by Minister Martin or anybody on his behalf in relation to his statements.
He said he believed Fianna Fáil would fare better under Mr Martin's leadership.
He said he would encourage other members of the Parliamentary Party to go public with their views of the leadership of the party too.
Mr Cowen this resumed contacts with members of his parliamentary party about his leadership.
He indicated that the process of consultation should be concluded by this evening.
Whatever Mr Cowen decides to do, his colleagues hope the decision will be made quickly.
Minister for Children Barry Andrews has said he will support whatever decision Mr Cowen makes about his future leadership of the Fianna Fáil party.
Speaking on RTÉ Radio One's Saturday View, Barry Andrews, who spoke to Mr Cowen yesterday, said he is sure Mr Cowen wants to do what is best for the country and for his party.
He said his understanding is that Mr Cowen is still taking soundings from parliamentary party colleagues and will make a decision, perhaps tomorrow, but certainly very quickly.
Mr Andrews said he would be happy to see Mr Cowen lead Fianna Fáil into the general election.
He said he doesn't think a change of leader will do the Fianna Fáil party any good and would not be good for Ireland either.
He added that it was completely wrong for people to think that Brian Cowen is responsible for Fianna Fail falling to 14% in the latest opinion polls. Mr Andrews added that Mr Cowen is not downbeat.
The Taoiseach had indicated the process of talking to members of the parliamentary party, which began on Thursday evening, could take up to 48 hours, so it may be concluded today - although it is not clear if he plans to make any statement this weekend about his decision.
Whatever the outcome of this process, the Government will face a Labour Party motion of no confidence in the Dáil the week after next.
However, Fine Gael has claimed the timing of the motion is ‘ill-advised’, saying it will give Fianna Fáil a chance to unite, instead of bickering over the leadership.