Fine Gael TD Lucinda Creighton has said she hopes a compromise can be struck between the Government parties over the matter of legislating for the X Case.
Ms Creighton said it was a very complex issue that the Government needed to get right, but that there were very different views between the two parties and also within the parties.
There was a very strong view in Fine Gael, she said, that the lives of both women and unborn babies should be protected and this was what the party was trying to do.
Ms Creighton said she did not want to pre-empt the outcome of Cabinet discussions, but said that efforts were under way to find a reasonable compromise that everyone could be comfortable with.
Patience was needed, she said, and everybody needed to be given a chance to engage in the debate and have their voice heard.
Meanwhile, Fianna Fáil leader Micheal Martin has said he does not believe there should be another referendum on the abortion issue.
Speaking to journalists at the party's Ard Fheis in Dublin, Mr Martin said he wanted to be constructive, and to approach the Government's proposals in a non-partisan way.
He said the debate on motions about the issue this evening would inform the Parliamentary Party in reaching a decision on the Government's legislation.
Asked about the possibility of a free vote, as proposed by Senator Averill Power, Mr Martin said his job was to bring the party to a position on the issue, and he expected that would be possible.