Fine Gael and Labour TDs said they are willing to consider proposals for a new protocol on representations relating to prisoners in the wake of the controversy over representations by Minister of State for Labour Affairs Tony Killeen.
However, Labour has warned that an outright ban on prisoner representations could be counterproductive and may make impossible inquiries about genuine miscarriages of justice or cases of suspected wrongdoing by State authorities.
The protocol is being put forward by Mr Killeen and party colleague Denis O'Donovan following a meeting with the mother of murder victim Robert Lynch.
The meeting with Nora Lynch at her home in Bantry, Co Cork, came after revelations that Mr Killeen and his office had sought the early and temporary release of Mr Lynch's killer, Chris Cooney.
The revelations caused considerable hurt and distress to the Lynch family, who were not aware of the representations.
Bantry-based Mr O'Donovan said he and Mr Killeen were now committed to examining what measures could be introduced to prevent against political interference in prisoner sentences.
He has also suggested the creation of an independent ombudsman to adjudicate on early releases, temporary releases and prisoner transfers. The Minister for Justice currently has ultimate authority on such decisions.
Mr O'Donovan said that while this could take some time, a protocol could be put in place for such representations.
This is to be discussed at a Fianna Fáil parliamentary party meeting next week but Mr O'Donovan has suggested that a cross-party protocol might also be appropriate.
Fine Gael justice spokesman Jim O'Keeffe said he believed "it does make some sense to have an agreement or code of practice in place that public representatives would adhere to".
"I'd say personally, though, that most TDs and Senators are already careful in relation to these types of representations".
Labour Justice spokesman Brendan Howlin said he would certainly listen to any suggestions from Fianna Fáil but he was concerned that there "must be balance" in any proposals brought forward. While Mr Killeen "clearly made a mistake", any initiative "must be based on balance and proportionality".
He said there were genuine reasons for representations on prisoners such as those relating to miscarriages of justice or wrongdoing by the authorities.
"I'm concerned that the system is being devalued by people who simply deal with representations in a pro-forma way," he said.
Meanwhile, Mr Killeen has said representations relating to a dissident republican prisoner were prompted by a request from the late Mgr Denis Faul in 2002, as part of an initiative to encourage dissidents into the peace process.
A request to move Michael Hegarty, who was jailed in relation to a bomb plot, was made by Mr Killeen on health grounds.