Sinn Féin has been accused of planning to hold "Trump-style" rallies rather than focusing on trying to form a left-wing government.
ianna Fáil and Fine Gael have criticised Mary Lou McDonald's party for a series of public rallies to be held in the next fortnight.
Fianna Fáil TD Thomas Byrne said: "These Trump-style rallies don't indicate a party that is seriously preparing for government."
Fine Gael junior minister Patrick O'Donovan claimed Sinn Féin "wants these rallies around the country to give out and shout and roar but in actual fact do nothing".
The remarks come as the first planned event takes place in Cork tonight.
Sinn Féin has rejected the criticism, insisting the rallies are taking place "in tandem" with continuing efforts to form a government.
Ms McDonald announced the plans for the public meetings saying that Sinn Féin wants to "bring the conversation about a government for change to the people".
There will also be events in Dublin, Newry, Cavan and Galway.
Meath East TD Mr Byrne likened the meetings to the kinds of rallies held by US President Donald Trump and argued that Sinn Féin was holding public meetings rather than making serious attempts to form a government.
He also claimed Ms McDonald was ignoring the issues raised by Fianna Fáil leader Micheál Martin in the Dáil last week. Mr Martin said he could not go into government with Sinn Féin because of its "efforts to legitimise a murderous sectarian campaign" of the Provisional IRA.
Ms McDonald responded, saying she "did not care" what he thought about her party.
Mr O'Donovan referred to the 24pc of first preference votes secured by Sinn Féin in the election and said many parties got more than that but ended up in opposition.
"Rather than having rallies, we'd be delighted if Sinn Féin went away and actually formed a government rather than blaming everyone else," he added.
A Sinn Féin spokesperson said the party had made it clear it would "talk to all parties and Independents about delivering a government for change".
They insisted the party would be doing that this week, starting with a meeting with the Green Party today.
The spokesperson added: "Are Fine Gael and Fianna Fáil now seriously suggesting that political parties should not hold public meetings?"
With Fianna Fáil and Fine Gael ruling out a deal with Sinn Féin, attention is turning to the prospect of a deal between the two Civil War parties with the support of the Greens or others.
Taoiseach Leo Varadkar is due to meet Mr Martin as early as tomorrow for preliminary talks. The Fine Gael leader has not been given a mandate by his party to enter government formation talks. He has said Fine Gael is preparing for opposition, but has not ruled out a deal as a "last resort".
Fianna Fáil TD Robert Troy suggested yesterday on RTÉ that compromise would be needed to form a government and this would involve assistance from Fine Gael.
He questioned if Fine Gael had fully ruled out facilitating a Fianna Fáil-led minority government and said: "There's an onus and responsibility on Fine Gael to do the right thing."
A Fine Gael source claimed his intervention was "arrogant" and said: "It's hard to see any basis for meaningful talks this week if Micheál Martin takes a similar approach when he meets the Taoiseach."