Independent TD Clare Daly has moved a motion to introduce a bill to allow termination of pregnancy where the foetus has a condition that is incompatible with life.
Ms Daly said the women affected by this were in the main going through much wanted pregnancies but had experienced a devastating diagnosis that the foetus would not survive.
She said Minister for Justice Alan Shatter himself had described it as an intolerable cruelty.
Ms Daly said women were forced to travel abroad in secrecy and could not bring the remains back.
She said the matter would not be addressed in this Government's lifetime unless legislation was moved now and brought to the Supreme Court for adjudication.
The issue is to be debated in private members' business.