Numerous Fine Gael Ministers referenced the difficulties in the party during the debate over the Protection of Life During Pregnancy Bill, which saw three TDs and one senator leave the party in the last Dáil.
Mr Varadkar did not express a view at Cabinet but said the Government had three options: do nothing, follow the Oireachtas committee's report or suggest an alternative proposal.
"It (the proposal) went further than many people may have anticipated, it certainly went further than I would have anticipated a year or two ago", he said.
The eighth amendment of the Irish constitution, introduced in 1983, gives an equal right to life to a pregnant woman and an unborn child.More news: Illini players preview Iowa game
Simon Harris, the health minister, will this morning update cabinet on his department's work on a new abortion law, which could come into effect if the Eighth Amendment is repealed in a referendum this year.
Speaking today, Minister for Justice Charlie Flanagan said the issue has been a "challenging and sensitive" one but that he supports the recommendations of the committee.
"It is, I know, very much a private and personal matter and there is a diversity of views on this matter in the cabinet, in the Oireachtas, in every political party and I think in nearly every family or household", the Taoiseach said.
Ms Sherlock also criticised the committee's recommendations.More news: LG's 2018 OLED TVs: It's all about the software this year
He's refused to reveal his own position, instead wanting to wait to see what question is put to people in a referendum. "But then again, perhaps not", Mr Varadkar said.
Leo Varadkar says there's strong agreement at cabinet that a vote on repealing the 8th amendment take place this year. I don't believe this is an issue that should be in our Constitution.
However, the Pro-Life Campaign criticised the moves towards a referendum.
The minister for Business, Enterprise, and Innovation, Heather Humphreys, said the issue was "complex and emotive" and that she would continue to consult members of her constituency, particularly women. So my party, the Fine Gael party, will discuss this at our special parliamentary party meeting next week. The Government wants to hold the referendum either in May or early June.More news: Donald and Melania Trump Had a Rockin' New Year's Eve
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