Micheal Martin offers to meet Independent Alliance
Fianna Fáil leader Micheál Martin has offered to meet the Independent Alliance to discuss how a minority administration could be formed.
No meeting has been arranged, but an Independent Alliance spokesman said a meeting on Saturday was a possibility.
On Friday, the second largest party, Fianna Fáil, rejected an offer of partnership government with Fine Gael.
Irish prime minister Enda Kenny has said his offer of a partnership government still stands.
It would involve Fine Gael, Fianna Fáil and independents.
Mr Kenny, Fine Gael, invited Mr Martin and 15 independent TDs to fresh talks early next week to discuss the proposal.
He said negotiations on forming a government could not continue indefinitely.
The talks are taking place almost six weeks after a general election produced a hung parliament, in which no party won enough seats to govern alone.
Fine Gael, led by Mr Kenny, remains the biggest party with 50 seats.
Both Fianna Fáil and Fine Gael trace their origins in the Irish Civil War, when their founding fathers were on opposite sides of a bitter dispute over the 1921 Anglo-Irish Treaty, which partitioned the island of Ireland.
The historic political rivals are both centrist parties but have never shared power in a state where coalition governments are the norm.
Irish state broadcaster RTÉ has reported that Fine Gael's offer of partnership government remained on the table, but added that no further talks are planned between the two largest parties.
It also said Mr Martin has told his party that he was in favour of a Fianna Fáil minority government.
Fianna Fáil had a successful election and more than doubled the number of seats they held in the last parliament, but still have six fewer elected members (known as Teachtaí Dála or TDs) than Fine Gael.
Sinn Féin is the third largest party with 23 seats, the Labour Party has seven TDs while smaller parties and independents make up the other 34 seats.