The Fianna Fáil parliamentary party has already ruled out a coalition.
An Offaly Fianna Fáil TD says Sinn Féin has a duty to find a compromise between left-leaning parties and form a government.
Barry Cowen feels it's incumbent on Mary Lou McDonald, after the party received 24 per cent support in the election.
Sinn Féin is due to meet independents and smaller parties today, with the Greens also involved in discussions, ahead of the Dáil's first sitting on Thursday - and after the Fianna Fáil parliamentary party last week decided it would not consider a coalition with them.
Deputy Cowen says his party is sticking to its commitment: