The Minister of State for Labour Affairs, Tony Killeen, is to consult party colleagues and the Government about the possibility of banning political involvement in prisoner sentences.
The move follows a meeting yesterday between Mr Killeen and Nora Lynch, mother of Robert Lynch, who was murdered in 1991 in Ennis by Chris Cooney.
Mr Killeen has been at the centre of controversy for the last two weeks over making representations on the cases of 10 prisoners, including four separate letters seeking the early or temporary release of Cooney.
Yesterday Mr Killeen travelled to Bantry where, along with local Fianna Fáil TD Denis O'Donovan, he met Mrs Lynch, who has been highly critical of the representations.
She had been unaware of the representations until they were reported on in the media last week.
Over the weekend she has demanded that a new system be put in place whereby politicians would have no involvement in the early or temporary release of prisoners.
Mrs Lynch said there had been a "very fruitful conversation for about an hour and a half".
She said she had "nothing to say" at this stage on the content of the meeting. "It's up to the politicians now - the ball is in their court."
Mr Killeen and Mr O'Donovan will now raise the issue with Ministers, including Minister for Justice Michael McDowell, and Oireachtas colleagues, in an attempt to establish what changes could be introduced to the current system.
It is currently common practice for representations to be made by TDs to Mr McDowell on behalf of prisoners and their families relating to temporary releases, early releases and jail transfers.
Under current legislation, the Minister for Justice signs off on all temporary and early releases.
The Fianna Fáil TDs will now seek to establish whether an independent ombudsman could be established to receive all representations from prisoner relatives on such issues, and whether the role of the Minister for Justice on releases should be transferred to an independent authority.
A spokeswoman for Mr McDowell said the Minister would be happy to meet Fianna Fáil TDs to discuss the issue.
Yesterday Mr Killeen said he would not be commenting in detail on the meeting.
Mr O'Donovan described the meeting as "very constructive" and that the family had made a "number of reasonable demands".
"I, along with Minister Killeen, gave a commitment that we would investigate the whole matter, and come back to them."
He said he hoped to contact Mr McDowell over the current situation and to discuss the issue with the Fianna Fáil parliamentary party.
He added that there may also be a move to reach a cross-party consensus on stopping all such representations.