The Anti-Austerity Alliance and People Before Profit has said it will propose legislation to repeal the Eighth Amendment in the autumn.
TD Ruth Coppinger raised the issue during Leaders' Questions in the Dáil this afternoon, in the aftermath of a critical United Nations report last week.
Ms Coppinger told Taoiseach Enda Kenny if the Government did not move legislation to deal with the issue, they would bring forward a bill in the autumn, allowing time for organisations to lobby intensely.
The Taoiseach said he would be bringing a memo to Government next week to allow for the setting up of the Citizens' Assembly in six months.
Minister for Health Simon Harris briefed ministers today on last week's United Nations findings on Ireland's abortion ban. The Government has 180 days to respond to the findings.
The response will be preceded by the setting up of a Citizens' Assembly and the Government is also considering setting up a special Oireachtas committee to consider the Assembly's findings.
Mr Kenny told Ms Coppinger in the Dáil that it was pointless rushing into a referendum unless there was consensus on change.
He said his view was that if there was a referendum in October, it would not be passed.
"People want to know, if you are going to take this out of the Constitution, what are you going to replace it with? It's a very genuine question, one that I have had problems with myself," he said.
Ms Coppinger described the Citizens' Assembly as a "three-way process to kick this down the road'.
Meanwhile, the Pro Life Campaign group has said the Government's decision to bring forward the setting up of a Citizens' Assembly on abortion is "a knee-jerk reaction to the disgracefully one-sided report last week from the UN Human Rights Committee (UNHRC) which set the rights of the unborn child at zero and ignored the devastating after-effects of abortion for many women."
Cora Sherlock said: "This Assembly is being set up with one purpose only and that is to pave the way for a referendum to strip the unborn child of its last remaining Constitutional protection.
"The Ministers who have been attacking the Eighth Amendment at every turn in recent days have totally abandoned the rights of the unborn child and the tens of thousands of lives that have been saved by the Eighth Amendment," she said.
The Electoral Act may have to be updated to take account of this year’s Census ahead of the Citizen's Assembly.
Using the Census details would allow the Assembly to be fully representative.
Mr Kenny has already said that the composition of the Assembly would have to be approached with care to ensure it was representative of a range of perspectives.