Sinn Féin has introduced a private members' bill calling for immediate legislation to implement the Supreme Court judgment in the X Case.
Introducing her party's motion, Sinn Féin's Mary Lou McDonald said the system has fudged and prevaricated for 20 years.
She said pregnant women continue to be left vulnerable with doctors left to operate in grey areas.
Pregnant women and the medical profession, she said, were being failed by politics and that is the truth.
Sinn Féin President Gerry Adams said his party was not in favour of abortion.
He said he was personally am not in favour of abortion. However, he said: "I am not mandated to come here to legislate for me."
He said in cases of rape, incest and sexual abuse, or where life of the mother in grave danger, the choice is with the woman.
Minister of State Kathleen Lynch appealed to the movers of the motion for calmer heads to prevail.
She said that the anger they feel was the anger people had felt down through the years, but we were not in sight of doing something very concrete about it. She said not acting was not an option.
RTÉ News understands that the Government will commit to immediate publication of a report by the expert group on abortion,
A Dáil debate to follow before the Government reaches decisions on the matter.
The commitment will be made during the debate on a Sinn Féin motion calling for immediate legislation to implement the Supreme Court judgment in the X Case.
The Government counter-motion will support the Minister for Health's recommendation that the expert group report should be published immediately after it is brought to Cabinet.
Ministers are due to discuss the report at a Cabinet meeting on Tuesday.
The counter-motion will also agree to have a discussion in the Dáil and Seanad on the report "over the coming weeks" in advance of a Government decision on the matter.
On today's Order of Business, Socialist Party Deputy Joe Higgins told the Dáil that it was a week since Health Minister James Reilly had received the expert group report on the ABC and X cases. He asked why it had not been published.
Deputy Higgins said the Government was treating it like one of the ‘Secrets of Fatima’.
The Taoiseach said it was patently obvious that there was a need to provide clarity in such medical situations. He said certainty was needed.
Mr Kenny said he wanted every member of the Oireachtas to have a chance to express their views and that this would help the Government to frame the necessary action.
He said the whips would be deciding how that debate will happen and what duration and shape it will have.