Mr Varadkar said there were diverse views at cabinet during a discussion about the likely referendum on the Eighth Amendment.
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.
In December, the Oireachtas Committee on the Eighth Amendment recommended that unrestricted access to abortion should be made legally available for the first 12 weeks of pregnancy. "Certainly, it went further than I would have anticipated a year or two ago", Mr Varadkar told journalists at Government Buildings.
However, Mr Coveney, who is seen as being on the conservative side of Fine Gael, will miss today's meeting as he is now on a tour of Israel and Palestine.
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The Washington Post reported on Thursday that the president made the remarks during an Oval Office meeting on immigration reform. The president said he has a wonderful relationship with Haitians and suggested future meetings probably should be recorded.
The Taoiseach has said he wants a referendum in May, and the Dáil will need to move quickly when it returns next week if they want to achieve that. "And I will advocate for people to vote on the lines of the views that I will express, but I'm not going to be ramming my views down anyone's throats", he said.
But also after reading the report I can understand the logic behind that and why they came to that decision, particularly given the widespread availability now of the abortion pill.
The Cabinet is meeting today to discuss the Oireachtas Committee report which was published just before Christmas.
The referendum is expected to take place early this summer.