Sinn Fein leader Mary Lou McDonald has criticised what she described as the "old boys' club of Fianna Fail and Fine Gael" as they have both refused to enter government talks with her party.
Ireland's largest party Fianna Fail agreed not to go into coalition with Sinn Fein following a four-hour meeting of its parliamentary party on Thursday.
The decision is likely to stop Sinn Fein entering power for the first time, as their leader Mary Lou McDonald said forming a coalition without them or Fine Gael would be "very, very tricky".
"Any suggestion that Fianna Fail and Fine Gael together suggest change is farcical - transparently farcical, Ms McDonald said in Dublin on Friday morning.
"I think it is actually quite disgraceful that the old boys' club of Fianna Fail and Fine Gael believe that they can set aside the democratic mandate of Sinn Fein and the electorate."
Fine Gael and Fianna Fail have repeatedly ruled out going into government with Sinn Fein, as talks continue this week to try to form a coalition government.
Fianna Fail won the most seats with 38, but Sinn Fein won 37 seats and the highest proportion of first preference votes following Saturday's general election.
On Friday morning, a Sinn Fein TD said it will be impossible for the party to form a coalition government without the support of either Fianna Fail or Fine Gael.
Sinn Fein TD Eoin O Broin told RTE radio Sinn Fein is still open to talking to all parties but said there are big policy differences between Sinn Fein and Fianna Fail.
"On Tuesday morning the broad progressive left had 66 TDs and that is not enough for government," he said.
"What we have been saying since then is we want a government led by progressive left policies."
When asked how Sinn Fein can form a government without the two largest parties, he said: "You can't.
"The most irresponsible thing to do is what (Fianna Fail leader) Micheal Martin has said - to say he won't talk to a party that now represents 24 per cent of the electorate."