Fianna Fáil leader Micheál Martin has said he would go into coalition government with Fine Gael.
He has also ruled out the possibility of going into government with Sinn Féin.
During talks with Fine Gael on Wednesday, he said there was a serious exploration of policies.
Fianna Fáil won the most seats in January's election with 38, one ahead of Sinn Fein, which had the highest number of first-preference votes.
Parties need 80 seats to form a government.
Ruling nothing out
Mr Martin said there was a serious realisation that there had to be a different approach to government and did not dismiss the idea of creating a rotating Taoiseach (Irish prime minister) with Fine Gael.
"We have ruled nothing in or ruled nothing out," he told RTÉ's Today with Sean O'Rourke.
"Fianna Fáil is upfront in saying that a government can be formed, but other political parties have to make decisions for themselves."
He said a lot of useful work could get done in the coming weeks and the formation of government does not need to take as long as 2016.
Mr Martin said he was not fazed by the idea of another election, but said the Irish public would not forgive them if there was a second election.
The Dáil (Irish parliament) is meeting on Thursday for the second time since the general election, but there will be no voting to elect a taoiseach.
Fianna Fáil and Fine Gael are holding hold parliamentary party meetings before the Dáil meets at 14:00 local time.
The result of the meeting could indicate whether talks about forming a government could commence soon.
Still preparing for opposition
Fine Gael's Paschal Donohoe has said his party were still preparing for opposition after initial talks with Fianna Fáil.
"There are many different governments possible in this Dáil which will rely on support from other parties," he said.
"Having an opportunity to hear the policies and ideas of other parties is beneficial of itself."
TDs are planning to establish a committee with the hope of making progress in reforming the Dáil.