The Dáil will later this month vote on a Bill that would allow for the termination of pregnancies in cases of fatal foetal abnormalities.
The newly formed business committee has agreed to debate a Private Members' Bill tabled by Independents TD Mick Wallace on June 30th.
The legislation will mirror that presented by his colleague Clare Daly last year. The very specific piece of legislation allows for an abortion to take place in cases of fatal foetal abnormality.
Under the measure, two suitably qualified medical professionals – a perinatologist and an obstetrician – would be asked to in good faith certify if the foetus is incompatible with life.
Mr Wallace and Ms Daly are in favour of repealing the Eighth Amendment to the Constitution, which guarantees the equal right to life of the mother and the unborn, but are eager to allow the Dáil its say on these specific cases.
The Wexford TD is understood to have consulted a number of legal advisers, including a former attorney general, before presenting the legislation.
His Bill has the support of deputies Thomas Pringle, Ms Daly, Catherine Connolly, Joan Collins, Maureen O'Sullivan and Tommy Broughan.
It is also likely to attract support from Sinn Féin, Labour, the Social Democrats, the Green Party and the Anti-Austerity Alliance-People Before Profit.
Taoiseach Enda Kenny has said Fine Gael TDs would have a free vote if and when the Government brings forward its proposal on a referendum but a senior Government source indicated there was unlikely to be a free vote on Mr Wallace's Bill – or any other – when it reaches the floor of the House.
Fianna Fáil members will be allowed a free vote but there are varying views within the parliamentary party on the issue.
There is a little evidence of support among many Fianna Fail TDs for a broader liberalisation of the law on abortion but there is a significant amount of support for abortion in cases of fatal foetal abnormality.
The Taoiseach has pledged to establish a citizens’ assembly to consider a number of proposed constitutional reforms and other issues.
He has said the question of the strict ban on abortion in the Constitution would be the first matter put before the assembly.
Depending on the recommendations of the assembly, the issue will then be referred to a special all-party committee before the question of any constitutional amendment is considered by the Government and the Dáil.
Mr Kenny is to bring a memo to Cabinet next week on the establishment of the convention, which Government sources say will be set up by September.
Ireland's position on abortion has been condemned by the United Nations Human Rights Committee.
It found that an Irish woman carrying a foetus with a fatal abnormality was subjected to cruel, inhuman and degrading treatment due to the ban on abortion.
It is understood the UN is considering a second case.
The committee said Amanda Mellet was forced in 2011 to choose between carrying her baby to term, knowing it would not survive, or travelling abroad for a termination.
