The measure was approved on first reading 138-24, The Irish Times reported.
Four representatives face expulsion from the governing Fine Gael Party for defying Prime Minister Enda Kenny and voting against the measure.
The bill would allow abortion only when necessary to save a pregnant woman's life. Its most controversial provision allows women at risk of suicide to seek to end pregnancies.
The measure would codify a Supreme Court ruling handed down 20 years ago. It was given new urgency by the death of a woman who developed an infection after doctors at a Galway hospital refused to end her pregnancy after she went into early labor because they could still detect a fetal heartbeat.
The Catholic Church opposes the bill.