The party’s junior health minister Kathleen Lynch insisted that repealing the Eighth Amendment, which gives equal weight to the life of the mother and unborn, was “do-able”.
But while senior Fine Gael figures backed getting rid of the amendment, they insisted that there could not be another referendum during the remaining lifetime of this Dáil.
Labour sees presenting itself as the agents of social change after the overwhelming endorsement of the marriage equality cause it championed as the best hope of the party avoiding a wipe-out in a general election which must be held by next spring.
Ms Lynch warned that the Eighth Amendment was the major roadblock to reform and needed to be removed.
“First and foremost we have to repeal that amendment to the Constitution and then sit down and legislate in a practical and reasonable fashion that will allow the people that treat women, when they find themselves in particular circumstances, to make decisions without that chilling effect hanging over them.
“I believe that if you’re forceful enough in your conviction, and I think we are, that repeal of the Eighth Amendment is very do-able,” Ms Lynch told RTÉ radio.
Referring to the “appalling circumstances” in which women with fatal foetal abnormalities find themselves, Ms Lynch said: “Unless we repeal the Eighth Amendment there’s very little we can do about that.
“It won’t be for everyone, it won’t be compulsory, but couples finding themselves in appalling circumstances... and having to travel abroad without the support of their families to have that remedy, it will be part and parcel of what needs to happen.
“And I don’t believe there’s anyone in the country that would deny that to people.”
Labour senator Ivana Bacik said the overwhelming yes vote in the marriage equality referendum would bring Fine Gaelers on board to support repeal of the Eighth Amendment.
“Labour led from the start on marriage equality and... Fine Gael moved to the same position. “The centre has moved on social issues.”
The Eighth Amendment of the Irish Constitution, which Health Minister Leo Varadkar says has a “chilling effect” on doctors, states: “The State acknowledges the right to life of the unborn and, with due regard to the equal right to life of the mother, guarantees in its laws to respect, and, as far as practicable, by its laws to defend and vindicate that right.”
Like Mr Varadkar, Minister for Children James Reilly said he wanted the amendment repealed, but said it could not be done this side of the election.
“It’s something that I will be working very strongly for and very strongly toward and while it’s very well to say repeal the Eighth Amendment I believe we have to address this issue... in a manner that doesn’t deliver abortion on demand because I don’t believe that’s what the Irish people want,” Dr Reilly said.