The Dublin cabinet met on Tuesday to discuss the bill, which has already caused divisions to emerge within Fine Gael.
Under the legislation, in a medical emergency, one doctor would be needed to approve a termination. In a non-emergency, that increases to two doctors.
If there is a risk of suicide, three doctors will be needed to sign off on the procedure - but this part of the legislation is proving difficult for Fine Gael members.
Up to 20 Fine Gael TDs and Senators could vote against the bill if it allows abortion on the grounds of suicide risk.
Current law prevents abortion unless there is a risk to the life, rather than the health, of the mother.
Taoiseach Enda Kenny had hoped the bill would be approved on Tuesday and sent off to the committee for the next stage of legislation.
He said: "This is about saving lives, about giving legal certainty and clarity. It's an issue that has been around for a very long time and it's necessary that we do that and provide certainty for women and certainty for medical personnel."
"It's about saving lives - the lives of the mothers and the lives of the unborn children."
Minister for Communications Pat Rabbitte added that Ireland has avoided this issue for too long.
He explained: "In the interests in particular of women, legislators - whatever their personal convictions in this matter - must have regard to the decision of our own Supreme Court and of the European Court of Justice and should do their duty as legislators and I hope that's what will happen."