RTÉ is to apply to the High Court seeking permission to broadcast statements made by Independent TD Catherine Murphy regarding businessman Denis O'Brien.
The issues raised by Deputy Catherine Murphy under Dáil privilege cannot be reported, as they are also the subject of a High Court injunction.
A spokesperson for Mr O'Brien said Dáil privilege had an important role in Irish society and democracy but it should not be allowed to be "used or abused where falsehoods are misrepresented as facts as has happened in the Dáil in the last 24 hours".
The RTÉ application will be made next Tuesday.
In a statement this afternoon, the station said it has "consistently maintained that greater levels of disclosure is in the public interest; however we have complied fully with the court’s decision.
"We await the outcome of the judge’s ruling on June 5 as regards what level of detail in the court’s judgement can be disclosed.
"Lawyers acting on behalf of RTÉ have already raised concern about the scope of the proposed orders to be made by the court.
"Every effort will continue to be made by RTÉ to report on this matter as comprehensively as possible, as early as possible, within the limits of the law."
Independent TD Catherine Murphy said that she stands by her right, as an elected parliamentarian, to utilise her democratic mandate to put information that has come to her in the public interest into the public domain.
Various Opposition leaders including Micheál Martin and Gerry Adams have called for the Dáil to be recalled to discuss the issue of parliamentary privilege.
Update: The Government Press Office has released a statement confirming that the Dáil will resume business on Tuesday June 9, as scheduled.
The Chief Whip will then consult with his counterparts in the Opposition on issues of concern, and ways for such issues to be debated in the House.