Opposition TDs have continued to criticise the "farcical" situation where Independents supporting the Government will get Dáil speaking time normally allocated to members of the opposition.
Some of the Regional Independent TDs involved in negotiating and supporting the Programme for Government have sought to keep their Dáil speaking time in opposition technical groups.
Ceann Comhairle Verona Murphy, who previously sat as a Regional Independent, has indicated that this will be allowed under parliamentary legal advice she has received from the Oireachtas.
Opposition parties have described the decision as “absurd”, objecting to the move on the basis that it would "eat into" their speaking time.
The row over speaking rights threatens to overshadow the first few days of the new government. The Dáil will meet from 11am on Wednesday where Fianna Fáil leader Micheál Martin will be formally nominated as taoiseach.
Social Democrats TD Gary Gannon said it was "farcical" that TDs who "constructed" the Programme for Government wanted to take opposition speaking time in the Dáil.
Speaking on RTÉ’s Morning Ireland on Wednesday, Mr Gannon denied he was "making a mountain out of molehill".
He said it was was a "ludicrous" scenario where people who had "literally constructed the government’s position" would also get to challenge the government.
Mr Gannon said it was important for opposition parties to have speaking time to challenge government policies.
"This is why this matters. It actually means that it removes a chance for us to forcefully stand up on housing, on disabilities, on public services."
People Before Profit TD Ruth Coppinger told the same programme: “I think everybody can see what's happening here, that instead of encroaching onto the government's speaking time, the people who are going to support the government are trying to take it from the opposition.
"It's clear that the government has decided that the election is over and now they're going to revoke the promises or the impression at least that they gave people."
Kerry TD Michael Healy-Rae said there was a precedent for Independent TDs supporting the government but also having opposition speaking rights.
Speaking on Newstalk radio, he said the Confidence and Supply Agreement between Fianna Fáil and Fine Gael in 2016 saw Fianna Fáil supporting the government while at the same time “holding them accountable”.
There was no difference between that situation and now, he said. “The only difference is that Sinn Féin and others have to shout and roar about something today and this is what they are going to do. They’re trying to make a massive big mountain out of a molehill.”
Mr Healy-Rae, who is set to become a junior minister in the new government, said the precedent had been set before. “Why should we change the rules? Nobody has changed the rules that allow this group to exist, but you would have to change the rules to stop them from existing.”
Tipperary TD Mattie McGrath described being an Independent TD without speaking rights in the Dáil as "a lonely place on the back bench", which was why he had accepted a "late" invitation to join the Regional Independent’s technical group.
Mr McGrath told Morning Ireland that he wanted to represent his constituents and to be a "ferocious critic" of the government when necessary, while also supporting positive measures that benefit the people of Ireland.
Sinn Féin TD Pearse Doherty described the decision not to allow his party leader Mary Lou McDonald speaking time in the Dáil on Wednesday as “arrogant and petty”.
Mr Doherty told RTÉ’s Morning Ireland it was "unprecedented" that a nominee for taoiseach would not be allowed to speak in the Dáil.
"Nominees for Taoiseach always had the right to actually speak in this section. And the only reason that this has happened is actually to exclude Mary Lou. It's petty, it's vindictive. Like why are Micheál Martin and Simon Harris actually sitting together and saying, you know, how do we stop Mary Lou from speaking and why are they going to this effort? There are enough problems within the state instead of trying to curtail the speaking time of the opposition.
"Because we are a party of opposition we will fight this government tooth and nail on all issues, whether it's housing, health, cost of living. And we've seen the programme for government. We know that hundreds of thousands of people are going to be abandoned and the largest number of Sinn Féin TDs that we've ever had over 100 years, are going to take this government on every single day."
Anyone who was concerned about democracy should be concerned about the Ceann Comhairle’s decision to allow temporary opposition speaking rights to the Independent TDs who were supporting the government, he said.
Michael Lowry was the "king maker" in all of this, he added. Mr Lowry had nominated Verona Murphy to the role of Ceann Comhairle, and now she had a big decision to make because standing orders were very clear, he said.
"You cannot be in a group in government supporting government at the same time. It simply cannot happen.
"We expect Verona Murphy to call this right. We expect her to act independently and to call this right. If she doesn't call this right, we will look at every single opportunity to pursue this issue. This cannot go ahead. This cannot be allowed to happen. It is a farce and it is a sham. It has never happened before."
On the same programme, Labour TD Duncan Smith expressed anger over the government's actions, which he described as an attempt to exclude the Labour Party and other left-leaning parties.
He criticised the incoming taoiseach Micheál Martin for allowing the Independent TDs to "dictate" the direction of the government, and warned that this could lead to a troubled Dáil.
"The people are angry about this. They may not know the details of business committees, the standing orders and all the rest, but they know when a stroke is being pulled. They know someone's trying to duck and dive and they are not happy with this. We're not happy with this."
Mr Smith said the Labour Party would not discount any avenue of action, including the legal route. "We'll take our legal advice and we'll see where we can go with it. We are really angry about this. We don't do the performative stuff in the Dáil. We are very serious about how our parliament works."
There was a political solution in the Dáil, he added. "The Ceann Comhairle has to see sense here. This is the first real test of her independence and her judgement.
"The Ceann Comhairle represents all TDs and should represent all TDs fairly."
Aontú leader Peadár Tóibín criticised the new government for its lack of urgency, comparing its level of activity with that of US president Donald Trump on his first day in office.
Speaking on RTÉ’s Morning Ireland, Mr Tóibín defended his party’s decision not to support a request from Sinn Féin in relation to speaking rights in the Dáil.

"A key part of democracy is the fact that when an elected representative is elected, that they have a right to speak in the Dáil. And if we were to fulfill the request by the likes of Sinn Fein and others, we would actually be taking away any speaking rights we would have over the next five years.
"Mary Lou is really upset at the moment because she's going to miss out on ten minutes speaking today. And yet she's asking us to go without speaking rights for five years. There's a complete lack of awareness here. And in reality, if the other opposition parties wanted to actually resolve this change, and the standing orders make it impossible to create the situation that we have.
"But at the heart of that is standing order reform, to make sure that every elected representative has a democratic right to be able to represent the people that elect them. And nobody seems to be talking about that.
"It is interesting that Sinn Féin feels that this is of such importance that it's necessary for us to withdraw from this technical group. Yet when we ask Sinn Féin, we say, yes, we will withdraw for sure. Just give us the speaking rights, share your speaking rights with us. They say no and they slink away."