Brian Cowen has said he will continue with his job as Taoiseach and Fianna Fáil leader and will seek a dissolution of the Dáil after the current budgetary process is complete.
Asked if he would lead Fianna Fáil into the next election, Mr Cowen said it would be an issue for the party to decide its leader.
Speaking at Government Buildings tonight, the Taoiseach was surrounded by Fianna Fáil members of the Cabinet as he made his statement.
Earlier, two Fianna Fáil TDs had called on Brian Cowen to step down as Taoiseach and party leader.
Dublin South East TD Chris Andrews said he was making the call in the light of developments of the past week and particularly today.
Mr Andrews said there should be consultations with the Opposition to find all-party agreement to get the Budget through.
He said if that was not possible there should be an immediate General Election.
It followed Cork North Central TD Noel O'Flynn's acknowledgement that he had written to Mr Cowen asking him to resign as Taoiseach and Fianna Fáil party leader.
In his letter to the Taoiseach, Mr O'Flynn said he had issues with Mr Cowen's 'leadership style' and 'ability to communicate with the public'.
Mr O'Flynn said that the citizens of Ireland, members of the parliamentary party, members of the Fianna Fáil organisation and supporters 'were misled' last week with the Government 'being in denial all of last week'.
Earlier this evening, Fianna Fáil TD for Dublin South Central Michael Mulcahy said the Taoiseach had the support of the party for now but that things could change tomorrow.
Today, Mary O'Rourke TD said that the Fianna Fáil parliamentary party should meet early in the New Year to discuss its leadership and future direction.
Speaking in Athlone, Ms O'Rourke said that while she believed the Taoiseach had credibility after receiving the support of his colleagues at European level, the appropriate time to discuss his leadership would not be until the Budget had been passed.
Fianna Fáil Junior Minister Sean Connick said the issue of leadership will have to come up when an election is called.
He added that he would not be in support of removing the Taoiseach at this point in time.
Meanwhile, former Defence Minister Limerick TD Willie O’Dea said that he had firm views on the issue of Mr Cowen's leadership, but said a party meeting would be the most honourable way to discuss them.
He also said that an earlier election (than January) is possible if the Independents vote against the Budget.
He said an alternative is an immediate election but that this was not the most desirable outcome for the public or the candidates.
But he added, quoting from John Kenneth Galbraith, 'in politics you often have to choose between the disastrous and the unpalatable'.
When asked, Fine Gael's Deputy Leader James Reilly said he did not know if there was any point in tabling a no confidence motion in the Taoiseach, as the stance of Independents and other parties in the Dáil would need to be known in advance of any such move.
Asked if he would consider tabling a motion of no confidence in Mr Cowen, Labour leader Eamon Gilmore said it was something the party would consider but he said the Taoiseach must know that his Government is now disintegrating.
