Tánaiste Eamon Gilmore has said he does not believe there will be any roadblocks to a referendum on same-sex marriage.
The proposed reform is expected to be discussed by the Dáil in the autumn.
Mr Gilmore was responding to yesterday's recommendation by the Constitutional Convention that same-sex marriage should be legalised in Ireland.
Minister for Justice, Equality and Defence Alan Shatter has said that he welcomed the wide-ranging discussion on the issue by the convention.
However, speaking on RTÉ's Morning Ireland, Mr Shatter said that the holding of a referendum was a matter to be discussed by Cabinet.
He said he believed that legislation to address issues such as the parentage and guardianship of children of gay couples was needed before any such referendum should be held.
Mr Shatter said there was a "reasonable prospect" that the Government would decide to hold a referendum before the next election.
Yesterday’s vote was 79 in favour and 18 against, with the rest expressing no opinion.
The decision was taken by 29 members of the Oireachtas, three members of the Stormont Assembly and 65 citizens selected by a polling company to represent a cross-section of the Republic's electorate broken down by age, gender and region.
The outcome is a major boost for the campaign for equality for gay and lesbian couples.
The Minister for Communications Pat Rabbitte has described the result of the Constitutional Convention as a very clear outcome.
Mr Rabbitte welcomed the decision and said he thought it was in keeping with what he described as the 'impulse of the Irish people' at this time.
He said that as the Government will take that report and respond to it after due consideration.
Asked whether he could see gay marriage being introduced in the lifetime of this Government, Minister Rabbitte said he thinks that would depend on the consideration that happens.
He said he would certainly like to see the Government being able to fit it into the schedule of Constitutional amendments.
Minister Rabbitte emphasised that there is a very heavy schedule there already in terms of commitments to reform.
He said they would have to consider it in the context of the schedule that is there at the moment.
However, Catholic Bishops have said that the move would make the roles of mothers and fathers completely irrelevant in the bringing up of children.