Taoiseach Enda Kenny has made a direct appeal to Fianna Fail leader Micheal Martin to support him in government.
The Fine Gael and Fianna Fail leaders are meeting 40 days on from the election and with neither party any closer to securing enough support to build some form of coalition or partnership.
Mr Kenny, caretaker Taoiseach after losing two votes on being head of the next government, said the symbolism of the 1916 centenary should be reflected in the efforts to strike a deal over the next week.
“I want to be as flexible and as generous and as negotiating as possible in this regard,” he said.
“It is of course not just about numbers but it is also about stability and building a relationship of trust.
The Dail was adjourned until April 14 to allow for further talks.
Mr Kenny said there had been 50 hours of constructive and worthwhile talks with 15 independent TDs but that he now wanted negotiations with Mr Martin on creating a “stable, lasting and effective government”.
“I remain fully committed to working to ensure that the people get a government that will work diligently and hard on their behalf and that will last the term,” he said.
“They did give a very different answer in their votes. It is our responsibility to see that we deliver an answer to that by way of putting together a government.”
Mr Kenny declined to speculate on whether a deal could be done in the next 10 days.
Following the Taoiseach’s invitation, Mr Martin said he expected independent TDs to declare soon whether they will support him or Mr Kenny’s party in a new coalition.
He also criticised expectations over potential government partnerships.
“Some countries with the highest standards of governance in the world regularly have minority governments which are enabled to be formed by opposition parties. The key to this is that their parliaments assume a more professional and accountable role,” he said.
“Everything does not rise or fall on whether or not there is an all-powerful executive.”
Mr Martin said it was nonsense that a government can only be successful if it knows it will win every vote.
The Fianna Fail leader also criticised other opposition parties, in particular Sinn Fein, which he said demanded others form a government so it could be denounced.
Three nominees for Taoiseach failed to get enough backing as the Dail met for the second time since the election.
Mr Kenny had support from 51 TDs, down from 57 in the first vote as the Labour Party abstained.
Mr Martin had 43 votes, and Ruth Coppinger, Socialist Party and Anti Austerity Alliance member, had 10 votes.
Some independent TDs, who have been courted by Fine Gael negotiators as they tried to build a coalition over the last 40 days, warned they would only wait another week to support an agreement.
Calls were made for the parliament to spend its time working to resolve the crisis in homelessness, with 5,000 families in emergency accommodation and hospital overcrowding with 525 people on trolleys waiting for a bed.
Sinn Fein president Gerry Adams called on Mr Kenny, as caretaker Taoiseach, to use his power to set up a cross party committee to deal with the homeless and housing crisis.
“It is a matter of some wonderment that it’s taken them so long to face up to the fact neither of them can be elected without the support of the other,” he said.
Richard Boyd Barrett, Anti-Austerity Alliance/People Before Profit TD, said the vote for a Taoiseach was a farce and an elaborate political charade.
“Coincidentally it’s now 40 days and 40 nights since the general election that this farce has continued,” he said.
“While Jesus Christ wandered in the wilderness contemplating the sins of humanity and maybe the need to save it, Fianna Fail and Fine Gael have left this country in a political wilderness, but not contemplating how they can save humanity but rather how they can pursue the drug of power and political office without any concern for actual substantial issues that affect our ordinary citizens.”
One group of independents, the rural five including Noel Grealish, Michael Collins, Denis Naughten, Mattie McGrath and Michael Harty, issued the deadline for a deal.
Mr Naughten said: “We need a five year government not one that is going to last five weeks or five months.”
He said he was extremely frustrated that Mr Kenny and Mr Martin did not hold face-to-face talks over the last 40 days.
“(It is) the last opportunity to do the right thing in the next week,” he said.