The 32nd Dail is due to meet for the first time tomorrow
The Agriculture Minister Simon Coveney says it may take another six weeks to form a new government.
Nobody will be elected Taoiseach when the 32nd Dáil meets for the first time tomorrow.
Fine Gael will put forward the current Taoiseach Enda Kenny - while the Fianna Fail leader Micheal Martin and Sinn Fein's Gerry Adams will also put their names forward to be the next Taoiseach.
It is expected tentative negotiations between Fine Gael and Fianna Fáil will begin before Enda Kenny departs for Washington early next week.
But Mr Coveney says whatever happens between the two major parties, there are still several weeks of talking ahead.
It comes as an MEP has suggested a long delay in forming a government could see "international concerns" about stability.
While the Sinn Fein leader says the Dáil should continue to meet over Easter, even if no government is formed.
Gerry Adams says if a caretaker government has to remain in place, it should still be held to account.
The party has tabled a series of motions for the new Dáil on issues such as water charges, and the redevelopment of Moore Street.
Deputy Adams says ministers will retain some power and should be scrutinised in how they use it.
And a member of the Independent Alliance says the group will put forward a nominee for Taoiseach.
Deputy Kevin "Boxer" Moran was speaking to Shannonside Radio.