Fianna Fáil leader Micheál Martin has said it is very unlikely that Sinn Féin will emerge with credible numbers to form a government.
He was speaking after having a "preliminary" meeting with Fine Gael leader Leo Varadkar today. It was the first meeting between the two leaders since the General Election.
Speaking to reporters, Mr Martin said that the "left wing alliance" that was "trumpeted" a week ago has not made any gains.
He said that during the meeting, Mr Varadkar reiterated the Fine Gael position that they are going into opposition.
Mr Martin said he told Mr Varadkar that Fianna Fáil had formed their negotiating team and had a mandate to engage with the Green Party, Independents, the Social Democrats and others.
He said the discussion was a preliminary one and that he made it clear it should be based around policy. He said Mr Varadkar did not reject anything at the meeting.
Both leaders agreed to meet again but no date has been set.
Mr Martin said people expect a government to be formed and that they wanted real change and real progress on a number of issues such as housing, health and climate change.
He said he will meet with the Green Party tomorrow, and that there will not be a government formed by the time the Dáil reconvenes next week.
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In a statement following the meeting, Mr Varadkar said that both leaders "exchanged views" on a number of items including housing, climate change, health, cost of living, the economy and taxation.
Mr Varadkar said that he encouraged Mr Martin's party to continue "engaging with other parties with a view to forming a Government", and that Fine Gael continues to prepare for opposition.
Fine Gael met eight of the nine TDs from the Regional Technical Group this morning. The meeting was described as a frank and honest exchange of views.
Both sides agreed to keep in contact.
The Fine Gael delegation comprised Leo Varadkar, Paschal Donohoe, Heather Humphreys and Martin Heydon.
Also a new Dáil Technical Group will be formally established later made up of Marian Harkin, Michael Fitzmaurice, Michael McNamara, Thomas Pringle, Joan Collins and Catherine Connolly.
Meanwhile, Sinn Féin leader Mary Lou McDonald has told a rally in Dublin tonight that Fianna Fáil and Fine Gael are engaged in a blatant and deliberate attempt to keep the party out of power.
She said a coalition of the two would not change things and would instead frustrate the change that people want.
Ms McDonald called on the two parties to engage with Sinn Féin and she said her party respected the mandate of others.
Around 500 party supporters attended the meeting in Liberty Hall.
Sinn Féin TDs Pearse Doherty, Louise O'Reilly and Eoin O’Broin also spoke along with vice-President Michelle O’Neill.
Additional reporting Sandra Hurley