AAA-People Before Profit Alliance want a referendum before the end of the year
Fianna Fáil TDs will be allowed a free vote, when a bill on fatal foetal abnormalities comes before the Dáil next week.
The proposed legislation surrounding abortion laws is being put forward by Independents 4 Change TD Mick Wallace.
However, it has not yet been decided whether Fine Gael TDs and other Government Independent TDs will be allowed to vote with their conscience.
Fianna Fáil's Barry Cowen says despite his party's free vote, he has concerns over constitutional issues.
Meanwhile, AAA-People Before Profit Alliance TDs are calling for a referendum on abortion to be held before the end of the year.
The 8th Amendment, which was put into the Constitution following a referendum in 1983, gives equal right to life to the unborn as to that of a pregnant woman.
A Citizens' Assembly is being set up to consider the future of the amendment.
But AAA-PBP TD Ruth Coppinger thinks the assembly is only being used to draft a replacement article.