Mary Lou McDonald has insisted her party will not back down on a row over speaking time allocated to Independent TDs who support the Government.
The Sinn Féin president said the ongoing row could be easily resolved when the Government accepts it “cannot turn democracy on its head”.
However, Taoiseach Micheál Martin has insisted it is not a black-and-white issue and said he would not be “browbeaten” into upending Dáil principles.
Efforts to appoint Mr Martin as taoiseach two weeks ago were delayed by a day after opposition parties disrupted proceedings in protest over the speaking time dispute.
Nine Independent TDs support the Fianna Fáil-Fine Gael government – seven from the Regional Independent Group and two Co Kerry brothers Michael and Danny Healy-Rae. Five of the nine are ministers of state.
The other four Independents, including Michael Lowry who led the regional group in the programme for government negotiations with the two coalition parties, want to be part of a Dáil technical group, which would give them speaking slots during opposition time.
Opposition parties have argued this would dilute efforts to hold ministers to account.
The Government has proposed a “hybrid” technical group in the Dáil that would allow its members to either support the coalition or not.
Mr Martin is expected to meet with opposition party leaders on the issue on Tuesday ahead of the Dáil reconvening on Wednesday.

Speaking in Belfast, Ms McDonald said it was essential the dispute is resolved.
She added: “The combined opposition has spoken and acted in a unified way on this because it is fundamental that you cannot be in government and opposition at the same time.
“It turns logic and democracy on its head.”
“There is a solution and the solution is for Michael Lowry and his colleagues to be afforded all of their representative time from the government benches.
“It is as simple as that. We have made that clear to the Taoiseach. We hope that we will meet as a combined opposition with him tomorrow.”
Ms McDonald said: “I am very hopeful that this matter can be resolved, but it will only be resolved when Micheál Martin and Simon Harris recognise that they can’t turn democracy on its head.
“The government has no right, no authority to encroach upon the democratic role of the opposition to hold them to account.
“They shouldn’t be trying to interfere in that.
“If they can finally accept that then we can have a resolution but, to be clear, we are not backing down on this.
“Sinn Féin is absolutely resolute, all of the opposition benches are equally so.”
However, speaking in Brussels, Mr Martin said there were “fundamental principles” involved.
He said that since 1932, opposition TDs had been supporting governments.
He added: “We have to accept one basic principle, groups have a right to form.
“No political party can tell another group they can’t form a group.
“It is a basic principle of freedom of association within the Dáil.
“I am worried about the Sinn Féin approach that it is either this or nothing.”
He added: “In the next Dáil if we were short four or five TDs, why would four or five opposition TDs surrender all their rights in order to facilitate the formation of a government?
“There is a balance here to be worked out.
“It is not as black and white as has been articulated by some commentators and by the opposition.
“There are fundamental principles here and I am not going to be browbeaten into upending those principles.”
The Taoiseach added: “I want the resolution to this.
“We are willing to negotiate a resolution to this, but not on the black-and-white approach that has been adopted by Sinn Féin.”