Independent TD Mattie McGrath has told RTÉ board chairman Tom Savage that he should resign his position.
Mr McGrath made the comments at an Oireachtas Committee hearing into the Prime Time Investigates programme, ‘A Mission to Prey’, which defamed Fr Kevin Reynolds.
Mr Savage said the Board, the Executive and the staff of RTÉ shared the anger and the dismay of the public, their representatives in the Oireachtas and the Government itself.
He said he accepted the findings of the BAI report, and that lessons had been learned.
Fianna Fáil TD Éamon Ó Cuív called for an independent review into the preparation, editing and balance of current affairs programmes on RTÉ television and radio.
"There could be a random selection of programmes and a look at how they were made."
The former minister said this should include how topics and panels are chosen and how tweets and texts are used.
Mr Ó Cuív wondered if the legal advice at the meeting on 25 May 2011 - when the decision was made to broadcast the programme - had advised against the broadcast.
"We were entitled to know what that advice was and how much the scandal had cost."
Later, Mr Ó Cuív said he has had reservations about RTÉ News and Current Affairs for 20 years.
Speaking on RTÉ Raidió na Gaeltachta's drivetime programme Glór Anoir about the appearance of RTÉ executives before the Joint Committee of the Oireachtas on Communications today, he said he would be demanding an independent inquiry into the way in which RTÉ produces its news and current affairs programmes.
Sinn Féin’s Martin Ferris told the committee that no financial settlement can compensate Fr Reynolds for what he and his family and friends suffered as a result of the programme.
Mr Ferris described the case surrounding Fr Reynolds as an utter disgrace.
Mr McGrath also described the Fr Reynolds defamation as "downright disgraceful" and said it was an attempt to chase salacious headlines.
Fine Gael TD John O'Mahony asked if there were victims in RTÉ who were being made carry the can for other individuals.
Legal privilege
The Broadcasting Authority of Ireland said it was a source of regret that RTÉ did not waive legal privilege between it and its in-house legal department, but said this did not constitute a failure to co-operate with the investigation.
BAI Chairman Bob Collins said, on the question of legal advice, RTÉ was asked to make all information available and it did so other than information it considered privileged.
The authority regretted that but ultimately, he said, irrespective of what the advice was it was the broadcaster who makes the decision to broadcast.
However, in his statement, RTÉ Director General Noel Curran said RTÉ was never asked to waive privilege.
"If we had felt that the investigation was being hampered, and if we had been asked in those circumstances to look at legal privilege, we would have.
"We were unaware of that until we saw the final statement of findings."
Mr Collins said he was confident the investigation was thorough and comprehensive and had access to enough information to form a judgement.
Tom Savage told TDs that a full year before 'Mission to Prey' was initiated, the editorial sub-committee of the RTÉ Board had a detailed meeting with the Head of News and Current Affairs and the Executive Producer within Prime Time Investigates.
He said the sub-committee received assurances that all the guidelines that were in place at the time on doorstepping and secret filming were being continually observed.
"We were told that was in place and working, and it wasn't," he said.
The Director General stressed that RTÉ needs to be sure that it does not overdo secret filming, and that the circumstances around doorstepping are exceptional; where there is a real fear the person will not make themselves available.
He said the guidelines had been tightened up, with greater responsibility put on managers.