David Cullinane, Sinn Féin's newly elected TD in Waterford, has said he did not believe Sinn Féin could go into government with Fine Gael or Fianna Fáil given the policies on which Sinn Féin had stood for election.
Speaking on RTÉ's Morning Ireland, he said that Sinn Féin's plan was radically different to that of Fine Gael and Fianna Fáil.
"We stood on a very strong policy platform on wanting to invest in public services. We stood as part of the Right2Change platform which is the opposite to what Fianna Fáil and Fine Gael were promising. You stand on a policy platform to want to get your policies elected.
"We made it very, very clear to the Irish people that we would not go into government as a minority party. We will honour that. We only want to be in government to bring about change and not to make the mistakes that the previous Left have done," he said.
Mr Cullinane said Fine Gael and Fianna Fáil should now work together.
He added that today is a good day for Sinn Féin and that the party is pleased with the gains made across the state.
Speaking later on RTÉ's News at One, Sinn Féin's Pádraig Mac Lochlainn, who lost his seat in Donegal, said that Fianna Fáil and Fine Gael should form a government because it would mean a right-wing government facing a left-wing opposition.
"It's very clear, absolutely clear what needs to happen – that Fianna Fáil and Fine Gael should form a government together and then we will have a conservative right-of-centre government versus a mostly left and progressive opposition. I think that would be healthy for Irish democracy and in the best interests of all our people," Mr Mac Lochlainn said.
He said Sinn Féin was not an establishment party and all TDs elected for the party want, at some stage, to be able to implement the policies for which they stood.
Mr Mac Lochlainn said Sinn Féin is willing to work with other left-wing elements, but only with those who want, ultimately, to be in government.
He said there are some people who do not want to be in government but Sinn Féin wants to change this country and he hoped in the near future the party would be in a position to do that.
"All of the TDs that were elected for Sinn Féin, they do not, we do not want to be in opposition. We want to be, at some stage, in a position to actually implement the policies and change the lives of the people we represent. We don't want to be howling at the moon. Sinn Féin are willing to work with people on the left but on the basis that we genuinely want to be in government," he said.
Mr Mac Lochlainn saidt he was disappointed to lose his seat but he was delighted to see Sinn Féin's success in the election.
He said he had been unfortunate in this election but he would be back in the Dáil at the next opportunity.
Mr Mac Lochlainn said he stood up for issues that are unpopular while in the Dáil and he made no apology for that.
Speaking earlier on RTÉ's Today With Seán O'Rourke, Eoin Ó Broin, Sinn Féin's newly elected TD for Dublin Mid-West, said Sinn Féin will go into the next Dáil in a constructive way and will support those proposing serious change.
However, he warned that if the next government remained wedded to the same social and economic policies of the past, then the change that people voted for on Friday will not happen.
Speaking on RTÉ's Morning Ireland, Billy Kelleher, Fianna Fáil's Director of Elections, said the party would not be "contracting or formally requesting" support from Sinn Féin in any form.