Tánaiste and Minister for Justice Frances Fitzgerald has said she believes there should be a referendum on the abortion issue next year.
She said her own view has always been that "the Constitution is not the place to deal with this very complex issue. It's best dealt with between a woman and her doctors.
"But of course you also have to have an appropriate legislative basis."
"My own thinking is that there should be referendum next year.
She said she felt that you would need to publish legislation before a referendum.
Over the weekend the Citizens' Assembly recommended an extensive liberalisation of the legal grounds on which abortion may be provided.
This evening, Minister for Social Protection Leo Varadkar has also backed a referendum in 2018 on the issue.
In a statement, he said: "Over the next few months, the all-party Oireachtas committee will consider the Assembly's advice and refine it into a proposal that can be put to the people. I believe that once this has been done, a final proposal should be put in a referendum in 2018 so that the people can have their say."
Fianna Fáil Health Spokesperson Billy Kelleher said a referendum could take place next year, if the confidence and supply agreement with the Government parties remains in place.
The assembly voted on Saturday to replace or amend the Eighth Amendment of the Constitution, which deals with the right to life of the unborn, with equal regard to the right to life of the mother.
Abortion has proven to be one of the most intractable issues in Irish politics. A look back on the challenges it has posed to previous govts pic.twitter.com/xRWuhpPXou— RTÉ News (@rtenews) April 24, 2017
Speaking this morning, Minister for Public Expenditure Paschal Donohoe said he believed the issue of abortion should be dealt with by the current Oireachtas.
He said he could not give a timeline for legislation on the issue. He said that would be looked at by an Oireachtas committee, which will be formed soon.
The minister said the committee will prepare a report that the Government will then consider.
Mr Kelleher said: "If the supply and confidence agreement sticks, in terms of people honouring it and primarily from the Government side, then you will have a referendum in the lifetime of this Dáil.
He is a Fianna Fáil nominee to an Oireachtas committee that is currently being assembled to assess and add to the work of the Citizens' Assembly.
Speaking on RTÉ's News at One, he said Fianna Fáil members will have a free vote on the issue. He said this is a conscience issue and individual party members will vote according to their view.
He said "the status quo cannot prevail" and "there needs to be an acceptance that issues have to change".
Sinn Féin's Health Spokesperson Louise O'Reilly has said the Oireachtas should "absolutely not" be bound by the findings of the Citizens' Assembly.
Speaking to reporters outside Leinster House she also claimed the Citizens' Assembly was only a "delaying mechanism".
She said the controversial abortion issue can no longer be kicked down the road and said "it's time to have the debate and the floor of the Dáil is the place for that".
Ms O'Reilly and Jonathan O'Brien will be the Sinn Féin representatives on the committee that will assess the Citizens' Assembly's work.
She said she wants to see the work of that committee begin as "there is an appetite for change and reform. We have the recommendations now. We have an opportunity. We have the committee. We need to get going on this."
Fine Gael TD Bernard Durkan earlier said a referendum on abortion will take place.
He said it was important that a rational and calm debate on the issue also takes place.
Independent TD Mattie McGrath has said there should be a referendum to allow the people of Ireland decide on the issue of abortion.
Mr McGrath said the outcome of the assembly was a huge disappointment, but not a huge surprise, adding that the process of establishing it was flawed.
He said there was no Assembly member residing in either his own county of Tipperary, or in Kerry.
The Tipperary TD said he is opposed to abortion in all circumstances.
Labour's Jan O'Sullivan said she agrees that there should be another abortion referendum.
Speaking on RTÉ’s Morning Ireland, she said that the Oireachtas committee considering the issue should get up and running as soon as possible, so it is ready to consider the final report by the Citizens’ Assembly once it is completed.
She added that it was clear the issue needed to be dealt with by way of legislation and she welcomed the fact that the assembly has acknowledged that the issue is a very complex one.
A spokesperson for the Pro Life Campaign described the Citizens' Assembly process as chaotic, muddled and "a shambles".
Cora Sherlock said that once you interfere with the Eighth Amendment, it would lead to abortion on demand and asked what this will mean for children in the future, adding there was no talk of restrictions in areas such as gender selection.
Speaking on RTÉ's Today with Sean O'Rourke, Ms Sherlock said she wanted the Oireachtas committee to really examine these issues.
She said the Eighth Amendment had been on trial throughout the whole process and this should not have been allowed.