The Minister for Transport Paschal Donohoe has said it is not tenable that the media outlets in Ireland cannot fully report on what has taken place in our Dáil while media outlets outside Ireland can and are.
He said he understands RTÉ and other media outlets are seeking to challenge this through the courts and that this will happen this coming week.
Speaking on The Week in Politics Minister Donohoe said process should be respected while it is under way.
He said the Oireachtas will debate the issue after next week's recess when the full view of the courts should be more apparent.
But Fianna Fáil spokesman Timmy Dooley said the Constitution sets out very clearly the provisions of Dáil privilege and the constitution should reign supreme.
He said the Dáil should sit on Tuesday or Wednesday and there should be a comprehensive statement from the Taoiseach outlining what he believes to be the situation, how he intends to protect the Constitution and the rights of the members of parliament as set out in the constitution and then let everybody have their say.
Mr Dooley said the Taoiseach has a responsibility to defend the Constitution.
Joe Higgins of the Socialist party said there was a staggering situation where a billionaire businessman who controls huge swathes of the media, then goes down to the High Court to silence the rest of the media about business dealings which he believes show him in bad light.
Meanwhile, speaking on RTÉ This Week, Independent TD for Kildare Catherine Murphy said she is confident of her sources in relation to information she received about businessman Denis O'Brien's dealings with IBRC.
A spokesperson for Mr O'Brien, James Morrissey has said the information, which was read to the Dáil on Thursday by Ms Murphy, was fundamentally wrong.
Ms Murphy said she would not have put on record something, if she had a serious doubt about it and that she believes what she did is in the public interest.
She said the Dáil should be recalled to clarify the matter in relation to media outlets reporting on the story and she said parliamentary privilege is there to protect public interest.
Ms Murphy said she believes she is not wrong in relation to the concerns she has on the matter and said she is standing over she has put on the Dáil record.
She said the aim of what she revealed on Thursday was to highlight the need for an inquiry into Denis O'Brien's dealings with IBRC and said the remit of the Comptroller and Auditor General needs to be widened in order to carry out the investigation.
Separately, Fianna Fáil leader Micheál Martin has described the silencing of the media as being in dangerous territory, where the alleged privacy rights of the powerful are coming into conflict with the fundamental Constitutional right of parliamentarians to articulate matters of undoubted public interest in parliament and to have those concerns aired and reported on.
Mr Martin said Dáil deputies or the Dáil cannot be silenced and that he has never experienced a situation like this.
He described a spokesperson for Denis O'Brien's response to the actions of Ms Murphy as an attack and said he had denigrated parliament by calling it a talking shop.
Mr Martin also called on Mr Morrissey to apologise to Ms Murphy for saying she is peddling lies and that she obtained information illegally.
He described the accusations as extraordinary and said it was an attempt to bully a parliamentarian, whom he said is held in wide respect across the political divide.
Mr Morrissey has alleged information she received and read to the Dáil on Thursday in relation to the businessman was false.
He said Ms Murphy has made statements that are fundamentally wrong and that documents she has were altered.
Mr Martin said it is absolutely essential that Mr Morrissey back off and said that the parliament cannot be undermined.
Responding to Mr Martin, Mr Morrissey said an individual is entitled to take a course of action to defend their privacy and that Mr O'Brien said at the outset, that he was taking the action against RTÉ broadcasting details of his banking affairs with IBRC as point of principle.
Mr Morrissey said the documents obtained by Ms Murphy were stolen from IBRC and altered before being handed over to the TD.
He said Mr Martin is relying on the totality of Ms Murphy's information without having seen the documentation.
Mr Morrissey said most of what Ms Murphy said in the Dáil was untrue but not all of it.
He said that he would have no problem with her presenting information that was true to the Dáil.
Labour Senator John Whelan said there is no point in recalling the Dáil before Tuesday.
Mr Whelan said the matter will be before the court that day and that the Dáil should only be recalled if the matter escalates beyond Tuesday.
Any TD, senator, editor or journalist could not be comfortable with the present situation, he added.
He said that he believes it is a contagion of censorship, whether it is by design or default, or whether it is by ultra or over-caution.
Mr Whelan said, never the less, it is in place, and it has silenced and gagged the media and effectively undermined the ability for TDs and Senators to do their job as protected by the Constitution.
He said this matter is way beyond party political issues and that it needs to be addressed.
Senator Whelan said if it is not resolved in the courts on Tuesday, that "we can longer sit on our hands and that we must take action".
Sinn Féin President Gerry Adams said this crisis stems from the Government refusing to heed the warnings of its civil servants that IBRC deals required greater attention.
Mr Adams said: "The attempt to gag the Dáil is an extension of the developing scandal surrounding IBRC and is another indication of the continuing and toxic relationship between big business and political parties such as Fine Gael and Fianna Fáil.”
Meanwhile, The Irish Times has confirmed it will be applying to the High Court on Tuesday morning (separately from RTÉ) to seek confirmation that Ms Murphy's statements can be reported.
The newspaper's editor, Kevin O'Sullivan, said: "We believe that to be the responsible and appropriate way to vindicate our right to report on these matters, and the public's right to know them."