The CervicalCheck Tribunal Bill 2019 has passed all stages in the Dail.
The proposed legislation would set up a tribunal for women affected by CervicalCheck to have their cases heard without having to go to court.
In the Dáil this evening, Labour's Alan Kelly appealed to the Minister for Health Simon Harris to accept an amendment to the bill, which would give women affected the right to pursue compensation if their cancer returns.
Earlier, the amendment was ruled out of order which Deputy Kelly said was "unprecedented".
Deputy Kelly said the Dáil was dealing with one of the most sensitive issues it has ever had to face.
He said women fear that when they have been treated the cancer will return.
In response, the Minister for Health Simon Harris, said he did not want to set up a tribunal that goes on "forever and a day" and that the women did not want that either.
Minister Harris said if cancer returned there was nothing to stop a woman taking a new cause of action to the courts.
He said the tribunal was a voluntary process which involved labs and the women affected and he said they needed both parties to attend.
Minister Harris asked: "Why would anybody go to a process that has a different rulebook to the High Court that you could continue to make multiple claims."
The Minister said he would not be happy to set up a tribunal that would not work and he said there were many benefits to the tribunal including hearings in private, written statements, and was also less formal and less costly.
The Minister said the amendment was not something that would be agreed on today but he said he would engage with the opposition to address the concerns.