Four candidates have stepped forward to try and succeed Brian Cowen as leader of the Fianna Fail party.
The move comes as both opposition parties say they will pursue a no confidence motion in both the prime minister and the government next week, which may move up the date of the election currently set for March 11.
Cowen stepped down on Saturday but remains as caretaker Prime Minister until after the next election.
The four are former Foreign Minister Micheal Martin, the favorite, current finance minister Brian Lenihan, current tourism minister Mary Hanafin and current social protection minister Eamon O Cuiv, grandson of party founder Eamon De Valera. The party election for leader will be held on Wednesday.
Fine Gael, the main opposition party have stated they will seek a motion of no confidence on Cowen as Prime Minister on Tuesday, saying his own party will not have him as leader yet they want to allow him to be Prime Minister.
The Labor party say they will move a no confidence motion in the entire government on Wednesday. If either succeed an immediate general election, set for mid to late February, would be called.
Fourteen members of the Fianna Fail parliamentary had voted to support Martin on Saturday night, making him the front runner. He had challenged Cowen for the leadership last week but had been defeated.
Then Cowen bungled a cabinet reshuffle which went badly wrong and was forced to resign.