In his Christmas message, the Catholic Archbishop of Armagh and Primate of All Ireland said there is no more important value than upholding the right to life in all circumstances.
As the Government prepares legislation giving effect to the X Case judgment, Dr Brady warned that we approach a defining moment regarding Ireland's attitude to respect and care for human life.
The death in October of Indian woman Savita Halappanavar, who was denied an abortion of her dying foetus, has intensified the debate around abortion.
"I hope that everyone who believes that the right to life is fundamental will make their voice heard in a reasonable, but forthright, way to their representatives," Cardinal Sean Brady said in his Christmas message.
"No government has the right to remove that right from an innocent person."
The Supreme Court ruled in 1992 that abortion was permitted when a woman's life was at risk but successive governments have avoided legislating for it because it is so divisive.
The death of Ms Halappanavar, who repeatedly asked for an abortion while she was miscarrying in University Hospital Galway, highlighted the lack of clarity in the law that leaves doctors in a legally risky position.
Ms Halappanavar's death re-ignited the abortion debate and prompted large protests by groups both in favour of and against abortion.
Cardinal Brady said public representatives will decide whether a caring and compassionate society is defined by providing the best possible care and protection to a woman struggling to cope with an unwanted pregnancy, or by the deliberate destruction of another human life.
The cardinal criticised the failure to prioritise the elimination of child poverty in the reform of the tax and welfare system, remarking that in any jurisdiction a failure on such a fundamental rights issue is unworthy of a society which claims to have a paramount concern for children.
That comment was a thinly-disguised challenge to the Government to deliver on its commitments in the Children's Referendum campaign.
The cardinal, who has faced calls this year to resign over accusations he failed to warn parents their children were being sexually abused, said in his Christmas message that he wanted relations with the Government to improve.
"My hope is that the year ahead will see the relationship between faith and public life in our country move beyond the sometimes negative, exaggerated caricatures of the past."