Fianna Fáil and Fine Gael have both said the onus is on Mary Lou McDonald to form a government.
Attention is now focused on the formation of a new administration after all the seats in the 33rd Dail were filled last night.
Fianna Fail's Thomas Byrne says the party are prepared to wait and see what the outcome of those efforts are.
He said: "The reason I'm stepping back from it during this interview is because Mary Lou McDonald has said we are her last resort.
"She is going to talk to left-wing parties, presumably, those talks are already happening or she is on the phone.
"Fianna Fáil is always willing to step up to the plate and I have outlined my difficulties and my party's difficulties with Sinn Féin but clearly the country needs a government and it needs an executive to function."
The outgoing European Affairs Minister Helen Mc Entee of Fine Gael also outlined that the responsibility to form a government rests with the Sinne Féin leader.
Speaking on Newstalk Breakfast, she said there is a majority for a left-leaning government.
She said: "Sinn Féin essentially if you look at the number of votes they have received but also this idea of vote left or transfer left, we know it would be very difficult, there would is a majority for a left-leaning government.
"This is essentially what people have voted for so I think the onus is on Mary Lou McDonald to form that type of government."
Coalition of the left unlikely
Meanwhile, Ms McDonald has reached out to other parties on the left to talk about forming a government.
She has spoken with Brendan Howlin, Eamon Ryan and the Social Democrats as we now know the full makeup of the Dáil.
Our Political Correspondent Seán Defoe has been crunching the numbers on possible governments:
To have a majority in the Dáil you need 80 seats, but there are no two parties combined can reach that number.
At least three parties will be needed to form a government.
So any combination of Sinn Féin, Fianna Fáil and Sinn Féin could mathematically make up the numbers if they added the Green Party's 12 seats.
However, Mary Lou McDonald's coalition of the left looks unlikely.
Adding together Sinn Féin, the Greens, Labour, the Social Democrats and Solidarity People Before Profit only gives you 66 seats.
Adding the six left-leaning independents gets you to 72.
If you added the so-called pragmatic independents who might do a deal, you could get to 78 seats, just shy of a majority.
That combination would then need at least two rural or right-wing independents to come on board, and would be relying on 14 Independent votes to pass anything.
It could take a long time for any combination of the current numbers to come together and form a government.