Minister for Education Norma Foley has said negotiators from Fianna Fáil and Fine Gael are "doing all they can" to put in place a government by 22 January.
Ms Foley - who is on the Fianna Fáil negotiating team - said there is an "absolute determination" among all those involved to agree a programme for government that can last for five years.
"We really want to get this done. We want the work to be done, we want it to be sustainable and the target is the 22nd of January if at all possible " she told RTÉ's Saturday with Colm O Mongain.
Speaking on the same programme, Fine Gael TD Martin Heydon - who is on his party’s negotiation team - said there is "broad agreement" between both parties, who are getting closer to putting together a draft programme for government.
"There is a pace there to them now, we made a lot of progress this week and we had a lot of late nights and early mornings too. We have a lot of work done between Fine Gael and Fianna Fáil and we have broad agreement on the challenges we face and where we want Ireland to be," he said.
Both TDs defended the decision to negotiate with the Tipperary North TD Michael Lowry, despite their parties supporting a motion in the wake of the Moriarty Tribunal’s final report in 2011, urging him to step down as a TD.
Ms Foley said the matter is "hypotheticial" and the matter "doesn't arise" as Mr Lowry ruled himself out of a Cabinet position.
Mr Lowry is leading negotiations on behalf of seven TDs from the Regional Independents group.
"When a government is formed, the government will be ministers and I don’t expect Michael Lowry to be a minister in the next Government," Mr Heydon said.
Ms Foley pointed to his democratic mandate as a poll-topper in Tipperary North.
"The final arbiter of who decides a seat in Dáil Éireann is the electorate of a constituency. We need to be clear that the Regional Independents are negotiating as a group, there is no single individual."
Sinn Fein TD Louise O’Reilly said Fianna Fáil and Fine Gael "seem intent on cutting a deal" with Mr Lowry.
"I would love to know at what point in the last 13 years the opinion of Fianna Fáil and Fine Gael in relation to deputy Lowry changed. My understanding is that all parties sported a motion which contained the words 'we believe deputy Lowry should consider his position and resign Dáil Éireann.’ To my understanding nothing has changed except for the need for additional votes."
Healy-Raes to meet FF, FG teams amid govt formation talks
A number of meetings are under way with a view to forming a government before the next Dáil sitting.
Independent Kerry TDs Michael and Danny Healy-Rae are due to meet the negotiating teams of Fianna Fáil and Fine Gael later this afternoon.
However, a number of sources have dismissed suggestions that a super junior ministry has formed part of these discussions to date.
Things moved significantly yesterday when the Regional Independent Group of seven TDs entered Government Buildings for their first formal discussions.
They presented a detailed policy paper paving the way for insensitive talks to get under way from this morning, which will see the teams going through those positions line by line.
The negotiating team led by Mr Lowry also includes the Galway East TD Sean Canney and Sligo-Leitrim TD Marian Harkin.
The Healy-Raes meanwhile met the Taoiseach and Tánaiste for more than an hour and a half yesterday.
But suggestions that a seat at the Cabinet table was discussed have been played down, with sources saying that is something for much later.
Talks between Fianna Fáil and Fine Gael have also intensified and both sides could be in a position to agree a joint document by next week.
But a four-part coalition made up of both those parties, the Healy-Raes and Regional Independents is now the focus.
There is a determination to have this in place before the Dáil next meets on 22 January.
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