Independent TD Michael Lowry has ruled out an opposition demand that his technical group be excluded from the Dáil's Leaders' Questions slot.
Both Sinn Féin leader Mary Lou McDonald and Labour leader Ivana Bacik said it was a red line that Mr Lowry's group cannot ask the Taoiseach and Tánaiste questions.
Independents, who have agreed to support the Government, want to form a technical group which would afford them speaking time and other rights from the opposition benches.
However, opposition parties say the independents want all the benefits of being part of the Government and all the benefits of opposition.
Government TDs are likely to try to push through plans to allow members of the Regional Independent Technical Group to form a "hybrid" group across both Government and Opposition.
The Dáil is due to return on Wednesday, but the dispute over the matter remains deadlocked and unresolved.
Taoiseach Micheál Martin said he would not be "brow beaten" over the row, adding that he wants a resolution to the matter.
Mr Martin said he had been in contact with the leaders of both the Labour Party and Social Democrats last night after indicating that that he is amenable to meeting opposition party and group leaders next Tuesday to try and find a solution.
The Taoiseach said he believes that the basic political principle that groups have a right to form in the Dáil cannot be denied.
That, Mr Martin said, is a basic principle of freedom of association.
Speaking as he arrived at an informal meeting of EU leaders in Belgium earlier, he said that since 1932 Opposition TDs have been supporting governments in some shape or form.
No one ever said the late Tony Gregory was a member of government even though he supported the government at the time, Mr Martin said.
He added that there is a balance to be worked out and that it is not as black and white as has been articulated by some commentators and by the Opposition.
However, the Sinn Féin leader and Labour leader have reiterated their objection to the participation of Government TDs , such as Mr Lowry, in Leaders' Questions.
Ms Bacik said it is "simply unacceptable" and Ms McDonald said such a scenario would be a "nonsense, a farce and an insult".
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Labour TD Duncan Smith said Opposition parties were still angry over the issue.
Speaking on RTÉ's Morning Ireland, he said: "Our anger against this hasn't diluted in any way. We’re not ruling anything out. I don't want this to be a threat, but it's now at leaders' level. Our leader, Ivana Bacik, with other opposition leaders, are trying to get the Taoiseach and Tánaiste to engage on this."
Mr Smith said the move by the independents has "absolutely obliterated the notion of new politics", and that ambiguity around standing orders needed to be resolved.
"It was stated in the Dáil that there is an ambiguity on standing orders, so the Government have admitted to that. Unfortunately, that seems to have been fudged to get the Taoiseach elected and they are going to push through this ruling which will put Michael Lowry in de-facto opposition. That is absolutely unacceptable to us.
"It's been a deeply frustrating two weeks for us in opposition," he added.
