Tánaiste Simon Coveney wants a two-thirds majority lock on any new abortion laws to prevent them being easily changed
The Health Minister says the Government expects to set a polling date for the referendum on the Eighth Amendment this week.
The vote is expected to take place in late May, although a polling date will not be set until the referendum legislation is passed in the Seanad.
Simon Harris this morning arrived at Leinster House for a Cabinet meeting, where ministers discussed the proposals for abortion legislation if the Eighth Amendment is repealed.
Tánaiste Simon Coveney wants the proposed legislation to include a two-thirds majority lock to prevent it being easily changed in the future.
It would mean any alterations to abortion laws in the future would need the support of two-thirds of the Dáil and Seanad.
Minister Harris said he is willing to consider inserting any clause in proposed abortion legislation that would reassure the public, once the proposals are workable.
He explained: "For a very long number of weeks I've been looking at all of these issues in great detail, and I'm very amenable to any clauses that we can insert to provide extra assurances and certainty to the Irish people.
"All of these things would be need to be considered legally, in great detail, to make sure they are workable. This isn't about any one individual politician - this is about women, it's about their doctors, and it's about enabling women in this country to receive the support and compassion they currently can't receive in Ireland."
Simon Coveney yesterday declared he'd changed his mind on the issue of abortion.
He now backs abortion for up to 12 weeks into a pregnancy, once there are "strict guidelines" in place when abortions are requested.
Cabinet ministers today focused on the general scheme of proposed abortion laws they will aim to introduce if the Eighth Amendment is repealed.
The Tánaiste will say a two-thirds lock system would make it impossible for any one political grouping to change the law.
It will be seen as a move to allay fears on the pro-life side that the proposed new laws would open the floodgates for 'abortion on demand', and avoid any creeping change on the issue.
A two-thirds majority would be more than Fine Gael and Fianna Fáil combined in the current Dáil.
However, some opposition TDs suggested such a restriction would be unconstitutional.
Social Democrats co-leader Catherine Murphy argued: "Each vote is of equal value.
"I think what he's proposing, if you were to take it to a logical conclusion, would actually require another amendment to the Constitution. I think he's got to really rethink that."
For Health Minister Simon Harris, meanwhile, today's meeting was about tightening up some of the policies we already know about.
What Ministers are considered this morning is the most detail we will have on proposed laws before the planned referendum on the Eighth Amendment, which the Government is hoping will take place in late May.
The draft laws propose allowing abortions to be carried out by medical practitioners through abortion pills up to 12 weeks gestation.
A three-day cooling off period will be required from when a woman seeks an abortion to when she gets the pill.
The scheme also says abortions after 12 weeks will only be available in exceptional circumstances - in cases of fatal foetal abnormality, or when there is serious risk to the health or life of the woman.
Reporting by Sean Defoe, Nicole Gernon and Stephen McNeice