There have been calls for cross-party support for the 'Fatal Foetal Abnormalities' amendment to the Protection of Life During Pregnancy Act.
The Protection of Life in Pregnancy (Amendment) (Fatal Foetal Abnormalities) Bill 2013 is due to be brought before the Dáil by Independent TD Clare Daly on Friday.
Terminations for Medical Reasons have called on parties not to use the whip system in this case and say they have received support from approximately 50 TDs since they began their campaign.
However, a spokesperson for the Minister for Health said that the bill cannot be accepted by Government because doing so would require a constitutional amendment.
In statement the spokesperson said that in December, Minister for Health Leo Varadkar expressed his view that laws should be amended to cater for these very sad cases.
For this reason, the statement said Ms Daly's bill cannot be accepted by government.
It said the minister looks forward to an open debate on Friday and encourages Deputies to speak freely and express their views."
Up to eight members of the Labour Party spoke at the parliamentary party meeting this evening in support of allowing terminations in cases of fatal foetal abnormalities.
The meeting was told that the Government can not vote for the bill as it would require a referendum.
The parliamentary party was also told that an internal party committee under Senator Ivana Bacik has been set up to look at the eighth amendment and issues such as allowing terminations in cases involving fatal foetal abnormalities and rape.
The committee is due to report back to the party's conference in February.
Three Labour members also expressed the view that the alcohol misuse bill should have gone further on the issue of sports sponsorship.
One Day More, which is made up of parents who received poor pre-natal prognoses for their babies, criticised what it said was the almost exclusive focus on abortion in the debate over how best to deal with a diagnosis.