Fianna Fáil leader Micheál Martin has said that his party, Fine Gael and the Greens could sign off on a programme for government within two weeks.
Speaking on RTÉ's Late Late Show, Mr Martin described the talks as "serious".
He said if negotiations were successful, a programme for government could be signed off on if "not by the end of next week but very shortly after that".
Fianna Fáil leader Micheál Martin has said that his party, Fine Gael and the Greens could sign off on a programme for government within two weeks @RTELateLateShow | https://t.co/K1EkdsbVlq pic.twitter.com/HGEUjEMRJn— RTÉ News (@rtenews) May 22, 2020
He said he "100%" could understand why the public were wondering why it was taking so long to form a government - adding there was an obligation to do so.
Mr Martin said it would be an "appalling indictment on politics" if a government was not formed given the Covid-19 pandemic.
He added: "I think we can put this together."
He described the relationships between the party leaders as "good and respectful, we understand each other's challenges".
Asked if the government formation talks failed would he consider dealing with Sinn Féin, Mr Martin replied: "I am not going to speculate on that."
He said he was not bothered by recent opinion polls, including the Business Post survey which suggested his party was standing at 14%.
Mr Martin said he wanted to dispel the "unfair myth" that the Green Party would be bad for Irish agriculture.
Asked about the suggestion that he was concerned he could be the first leader of Fianna Fáil who did not become a Taoiseach, Mr Martin said: "I don't buy that."
He said of the general election, in which his party won 38 seats: "I was very disappointed. It wasn't what I expected but we are still the largest party in the Dáil."
The Fianna Fáil leader said he has not seen his family in "six or seven weeks" due to Covid-19 restrictions, which have left him in Dublin and his family in Cork.
He observed that while he spent a long time in Leinster House, it meant he had not "really discovered Dublin" but was now walking the streets and doing laps of Merrion Square.
Asked if he was Taoiseach in a few weeks' time, would he be nervous? "No, the important point is to get a programme for government that works."
The @fiannafailparty leader @MichealMartinTD has said the economic situation, due to Covid-19, is 'very serious' and Ireland could expect 'very high levels of unempoyment between now and Christmas.' @rtenews— Paul Cunningham (@RTENewsPaulC) May 22, 2020
The Fianna Fáil leader said the economic situation, due to Covid-19, is "very serious" and Ireland could expect "very high levels of unemployment between now and Christmas".
Asked about Covid payments, Mr Martin said they would be phased-out, adding this "won't happen immediately" and he hoped that "quite a lot of sectors will be back by then".
He said the roadmap to open-up the economy, and society, is flexible and some areas of the economy could be opened faster than the plan.
Mr Martin said there was "a lot of uncertainty" and added that "small and medium sized enterprises are the ones I fear most about".
He said shutting down the economy was "easier than opening it up".
On problems in meat plants, and clusters of infections, the Fianna Fáil leader contended that the State should publish where they occur, remarking: "I think human bevahour is better served by transparency."