Health Minister Simon Harris will today tell his colleagues that in order for a referendum to be held on May 25 or June 1 he must begin work on potential new laws immediately.
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.
Independent TD and Minister of State Finian McGrath said attention must be paid to the disability element to the debate, while Minister for Transport Shane Ross suggested no legislation on abortion should proposed until after a referendum to repeal the eighth amendment is passed.
The Cabinet will meet tomorrow for the first time since the publication of the report from Oireachtas Committee on the Eighth Amendment of the Constitution.
"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.
It called for gestational limits for abortion to be guided by the best available medical evidence and be provided for in legislation.
Ms Sherlock also criticised the committee's recommendations.More news: Security ramped up at fire damaged ACC Liverpool vehicle park
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Mr Varadkar would not be drawn on his own view and said he would have to see the referendum question first.
Labour leader Brendan Howlin urged Mr Varadkar to bring the proposal to hold a referendum to the Dáil as soon as possible.
He added that when he makes his decision he will advocate along the lines of how he is voting, and said ministers would be free to campaign on either side of the debate.
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.
The Committee's recommendations are likely to be discussed by the Taoiseach and his ministers ahead of a special meeting of the Fine Gael parliamentary party next Monday afternoon.
"I believe it is important now in the context given in the partnership programme for government that we move on towards the next stage".