Fianna Fail leader Micheal Martin has said he is prepared to go into government with Fine Gael.
The two parties met on Wednesday to “exchange views” on policy matters.
The latest meeting between the two came as agreement between any parties to form a new Irish government following last month’s general election remained elusive.
Asked by RTE radio if he is prepared to go into coalition with Fine Gael, he said: “Yes, depending on a programme of government that works and represents a new direction in terms of housing, health and climate change.”
However, finance minister Paschal Donohoe restated on Wednesday that Fine Gael’s preferred position remains to be in opposition.
Mr Martin ruled out speaking to Sinn Fein and said a left-wing government led by the party is not possible.
“The left-wing alliance is not going to materialise in terms of the numbers needed. That seems to be evident from the past two weeks. The realpolitik has to break through at some stage.”
Mr Martin said if government talks continue to stall, he is not afraid of a second election, but added that the public “would not forgive” the parties.
“I’m not scared of another election… we’re not fazed by that. However, I have always been of the view that there is an obligation on politicians to work to form a government.”
He added that when there were a number of successive general elections in the 1980s, “it was not conducive to good government”.
The Dail will meet on Thursday for the second time since the general election.
Fianna Fail and Fine Gael will hold parliamentary party talks before the meeting.
A vote for taoiseach will take place in two weeks’ time at the next Dail sitting on March 19.
TDs from across the country who form the Regional Group said it “was imperative” that there was a vote held for the election of a taoiseach, four weeks after the first inconclusive vote.
In a statement, the group said: “We hope that this two-week deadline will help focus the minds of Fianna Fail, Fine Gael and Sinn Fein on the urgent need to form a stable and effective government to address the issues facing the country.”