Fine Gael and Fianna Fáil are to meet early next week to discuss the possibility of a viable minority government, according to the Irish Examiner's Fiachra O Cionnaith.
The intense rivals confirmed the move in separate statements this evening after six weeks of deadlock since the February 26 general election.
The parties' negotiating teams met this morning for what both described as "exploratory" talks over how an end to the political stalemate can occur.
While an agreement has still not been reached, in almost identical statements they have agreed to hold further talks "early next week" on how a "viable" minority government could work.
"Following exploratory talks this morning, Fine Gael and Fianna Fáil negotiating teams have agreed to meet early next week to discuss how a viable minority government would work," the first statement from a Fine Gael spokesperson read.
The second, from Fianna Fáil leader Micheál Martin minutes later in what appears to have been a choreographed schedule, confirmed: "Following exploratory talks today, Fine Gael and Fianna Fáil have agreed to meet next week to discuss how a viable minority government would work.”
The moves comes less than 24 hours after an Independent Alliance bid to force caretaker Taoiseach Enda Kenny and Mr Martin to take part in round table talks which ended in another round of bitter acrimony.
Mr Kenny responded to the request by calling his own meeting with all Independents and Mr Martin but insisting the only issue up for discussion should be his now rejected equal partnership government plan.
Mr Martin similarly rejected the Independent Alliance's proposal, saying he is happy to talk to them but not as part of round table talks with Mr Kenny.
The stand-off follows weeks of stalling between both parties over how a government could be formed.
However, this evening's development indicates that at least some of this week's issues have been a smokescreen before genuine discussions on a minority government begin.
While Mr Kenny stood firm on his equal partnership plan last night, a number of Fine Gael ministers privately briefed the Irish Examiner over how a viable Fine Gael minority government would work.
The aim, it is claimed, is to get a minimum of 10 Independents - Michael Lowry, at least five of the Independent Alliance's six, Maureen O Sullivan, Katherine Zappone and the Healy Rae brothers - before seeking opposition support from Labour, the Social Democrats and the Greens.
This position would then be put to Fianna Fáil to support from opposition.
Any deal, a number of Fine Gael ministers have said, would be based on a written guarantee the minority government would be allowed to sit for at least two budgets.
Fianna Fáil figures have suggested they may allow a Fine Gael minority government, with commentators arguing it would suit Mr Martin's party as it allows them to remain in opposition to block Sinn Fein's progression while putting Fine Gael in charge of a weak government.
On Friday evening, Fianna Fáil's finance spokesperson and negotiating team member Michael McGrath publicly called for a toning down of rhetoric from both leaders and for calm heads.
He said the current stand-off was going around in circles and that he would be happy to speak with Fine Gael about forming a minority government.