Fianna Fáil leader Micheál Martin has said that he has met with a number of independent TDs and plans to meet with other political parties next week.
All three of the major parties have been holding their first parliamentary meetings since General Election 2024.
The separate gatherings of Fianna Fáil, Sinn Féin and Fine Gael mark the beginning of the process of negotiating the next coalition government.
Meanwhile, a Dáil group has been formed by eight Independent TDs which will give them speaking time in the chamber as well as positions on Oireachtas committees.
Speaking on RTÉ's Six One following the Fianna Fáil parliamentary meeting, Mícheál Martin said it is "early days yet" but added that his meetings with independents have been "constructive".
"I just wanted to get their perspective but what I drew from the conversations was that they are in solution-driven mode," he said.
Mr Martin said the Government will need a majority that goes full term, adding that he was "heartened" to see that this was the mindset of a number of the independents who he has met with so far.
"Ourselves and Fine Gael have won the largest number of seats, we're not that shy of a majority, and I think we must reflect the decision of the people," he said.
"I think it has to be reflected in policy and in the programme for government and in the configuration of government itself. But we're open to discussions obviously with the other parties."
Mr Martin added that his party was also open to discussions regarding a rotating Taoiseach.
Minister for Finance Jack Chambers has been appointed as the party's lead on negotiations on government formation.
Fianna Fáil has achieved the highest number of seats in the General Election, with 48 TDs.
On suggestions that Fianna Fáil would want a concession from Fine Gael given that it has ten more TDs, Mr Martin said his party had secured a very significant number of seats.
"That has to be reflected ultimately in the configuration and composition of policy and structure of government," he said following his parliamentary party meeting earlier today.
Asked about his contacts with Fine Gael leader Simon Harris, he said they had some initial contact and would see each other again on Friday at the British-Irish Council Summit in Edinburgh.
Mr Martin said Mr Chambers would lead the negotiations on government formation while outgoing ministers would come into talks relevant to their portfolio.
The parliamentary party members will also feed into discussions.
Following the General Election, Fianna Fáil has finished up with 48 TDs, Sinn Féin with 39, Fine Gael with 38, 16 Independents, Labour with 11, 11 Social Democrats, PBP-Solidarity with three, Aontú with two, Independent Ireland with four, Green Party with one and the 100% Redress Party has one seat.
Mr Martin has said most of the work can be completed by Christmas, but it will be the New Year before there is a final agreement.
The Fine Gael parliamentary party has also met for the first time since the election and agreed unanimously to give party leader Simon Harris a mandate to engage in government formation discussions.
Mr Harris has appointed Fine Gael's deputy leader Helen McEntee and Paschal Donohoe to lead the negotiations with other parties.
The group will report back to their party colleagues, in due course, with recommendations for the parliamentary party to consider.
"Following a two-hour meeting, party colleagues agreed to take their mandate forward on a basis of mutual respect, parity and crucially, on key policy agendas, to lead our country forward and continue working for people," a Fine Gael spokesperson said.
The next Fine Gael parliamentary party meeting takes place on Wednesday 18 December - the day the Dáil is due to reconvene.
Earlier, Mr Harris echoed Mr Martin's comments, saying he was was very open to engaging with Independents as well as smaller parties in the Dáil around formation of government.
He told reporters that he would not engage with Sinn Féin, saying that many voters in the General Election voted for a scenario where Fine Gael and Fianna Fáil would provide a stable government with others.
"We need to approach this from a point of mutual respect, from a point of grounding those discussions in policy, in deliverables, in reflecting what we heard from people across the country and what we set out in our manifestos".
He added that it was an exciting time of renewal for his party.
"We have brought new experiences, new energies and new insights to our parliamentary party, and (I am) really looking forward to having our first opportunity to engage today and then an opportunity in the days and weeks ahead to look at how we can put forward a government that can serve this country well, that can be stable, that can deliver five budgets, and that can navigate the choppy waters that may lie ahead."
Sinn Féin leader Mary Lou McDonald said it does not sit well with people that Fianna Fáil will not discuss government formation with her party.
She accused Mr Martin of ignoring the votes of hundreds of thousands of people and said she will seek to discuss this matter with him.
Ms McDonald said her party would continue to push for change and would never give up on creating a fair and united Ireland.
When asked about the comments on RTÉ's Six One, Mr Martin said that there was a "clear choice in the election".
"The people have voted and I do believe people have voted to retain and support the economic model fundamentally that we have in the country, which I don't believe Sinn Féin gets or supports," he said.
Meanwhile, the Social Democrats held an online parliamentary party meeting yesterday while the Labour Party holds its meeting tomorrow.
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Meanwhile, Sinn Féin's Louise O'Reilly said it is up to Mr Martin to decide who he wants to form the next government with.
Speaking on RTÉ's Today with Claire Byrne, the TD for Dublin Fingal West said her party wanted to be in government and would speak with anyone, but will speak to the parties on the left first.
"We are going to have a discussion with them about how we best advance the programme for change because all of those parties went to the people on the basis of delivering change for the people of this State, we did as well."
Speaking on the same programme, Independent TD for Dublin Mid-West Paul Gogarty said Fianna Fáil and Fine Gael are focussed on numbers at the moment, adding that Fianna Fáil-Sinn Féin coalition might offer people some change.
"I think Mary Lou is in the driving seat here, she should absolutely, and categorically say Sinn Féin wants to be in government we will talk with Fianna Fáil, if necessary because we want to implement policies rather than shout from the side of the ditch."
Additional reporting by Sandra Hurley, PA
