The Broadcasting Authority of Ireland is to investigate the circumstances that led to false allegations being made against Fr Kevin Reynolds by RTÉ.
The Cabinet discussed the matter this morning and decided that there should be "an independent inquiry to determine the true facts and circumstances" that led to the programme being broadcast.
Minister for Communications Pat Rabbitte has asked the BAI's Compliance Committee to examine if RTÉ "met its statutory responsibilities around objectivity, impartiality and fairness".
The Government said it expects a report to be delivered within two months.
RTÉ Director General Noel Curran has said the libelling of Fr Reynolds was one of the gravest editorial mistakes ever made in RTÉ and serious errors were made.
Asked if anyone would resign, Mr Curran said recommendations would be brought forward to the next RTÉ board meeting due in December. He said nothing was ruled out.
Speaking on RTÉ's Six-One News, Mr Curran said it was waiting for the outcomes of internal reviews before making these recommendations.
He said he was not directly involved in decisions to broadcast the programme.
On the reporter Aoife Kavanagh's direct response to solicitors' letters, Mr Curran said that was not RTÉ policy and was one of the issues being examined.
Mr Curran said the next series of Prime Time Investigates, which was due in December, has been suspended until the internal reviews and Professor John Horgan's review have been completed.
On the Government inquiry, he said anything that helped restore trust and confidence in RTÉ's current affairs and Irish journalism was welcome.
Mr Curran said the Government was perfectly within its rights to do this and that RTÉ has a good working relationship with the BAI.
The Association of Catholic Priests has welcomed the announcement of an investigation.
Spokesman Fr Sean McDonagh said the decision was a proper one because the injustice done to Fr Reynolds was so serious.
Fr McDonagh said the investigation would be an opportunity to review the perceived anti-Catholic bias within RTÉ and the media in general.
He said the association did not want to scapegoat any individual involved in the offending Prime Time Investigates programme nor did it want to see the end of robust investigative reporting.
Bishop of Elphin Dr Christopher Jones also welcomed the announcement that the Cabinet had discussed the matter.
Speaking earlier, Fine Gael Senator Michael Mullins said large amounts of taxpayers' money had to be spent in order to repair the damage done as a result of the programme and he said the minister should cut funding to RTÉ appropriately.
Senator Mullins said irreparable damage had been done to Fr Reynolds' reputation and he said there were other allegations of defamation in the programme against a person who is now deceased.
He said he had been provided with information that calls into question the basis on which the programme was made.
Fine Gael Senator Martin Conway has called on Senator Mullins to hand over the additional information to gardaí.
Senator Conway said the information should be made available for a criminal investigation to be conducted.
He said it was time for serious reflection on the powers of the press in general.
Independent Senator John Crown called for information on who imposed a 'gagging order' on the terms of the settlement.
He said public bodies should be prevented from imposing such orders.
Reynolds: RTÉ must face consequences
Speaking to Shannonside Radio this morning, Fr Reynolds said those at the heart of decision-making at RTÉ have to face the consequences of their actions.
Asked whether he would like to see disciplinary action in RTÉ over the libel case, Fr Reynolds said he was not out for anybody's blood or looking for people to be sacked.
The priest, who is based in Ahascragh, Co Galway, said he would leave the issue in the hands of his solicitor.
He said people in authority who have been appointed to State institutions and people at the heart of decision-making in RTÉ have to face the consequences of what happened and they are doing that now.
Fr Reynolds said he was grateful to neighbours and friends for their support during his ordeal.
When he was asked to stand down from his ministry, Fr Reynolds said it was as if everything he believed in and had achieved had gone down the swanee. "It was all over. I was destroyed."
He said that what upset him terribly and was very sad was that such distress was inflicted on his family and his parishioners.
Asked about whether priests are currently getting a tough time in the media, he said it was a hard life and he was living in a different Ireland now than the one in which he had been ordained.
"We are living in a secular society in which priests have been pushed to the sidelines."
However, Fr Reynolds said a lot of priests had telephoned him over the weekend to say they felt that they had been given a boost of confidence and he added nothing could compare to what the Catholic Church has to offer.