Mark Kelly of the Irish Council for Civil Liberties has called for the "swift enactment of the necessary legislation so that same sex marriages can actually start to happen."
Mr Kelly was speaking at a joint press conference held by the leaders of the three civil society groups behind the Yes Equality Campaign: The ICCL, Gay and Lesbain Equality, and Marriage Equality, alongside the co-directors of the campaign.
The Tánaiste and Minister for Social Protection Joan Burton told RTÉ News the draft legislation was ready and that it had been fully discussed at cabinet.
Ms Burton said: "I hope that we will be able to put it before the Dáil and Seanad as soon as possible, and the aim would be to have it completed before the Dáil rises for the summer."
She added the law requires that people who get married in Ireland are required to give a number of months’ notice.
"And so I anticipate and hope that we will be seeing a lot of marriage celebrations both gay and straight in the autumn", she added.
Ms Burton also said Ireland is now a nation of inclusion and diversity, following the passing of the marriage referendum.
Speaking on RTÉ's The Week in Politics, she praised the role of her predecessor Eamon Gilmore in putting marriage equality on the Government agenda.
She said the former Labour Party leader played a key role.
The Department of Justice published a draft of the General Scheme of Marriage Bill 2015 in March.
The department now intends to publish the marriage bill itself shortly.
This will have to pass through both houses of the Oireachtas.
It is the department’s Intention that it will be enacted before the summer recess.
Mr Gilmore said Ireland has an obligation to use what he called the mandate from Yes decision in the referendum to become international advocates of gay rights.
Speaking on RTÉ’s This Week, Mr Gilmore also said the Government needed to address the concerns of the No campaign regarding the issue of surrogacy and also called for legislation to deal with the area of commercial surrogacy.
At it Happened: Ireland backs same-sex marriage
Meanwhile, Catholic Archbishop of Dublin Diarmuid Martin has said a trial project is needed in parishes to find a way in which to reconnect the church with young people.
He said he asked priests in Dublin in recent weeks to identify five parishes out of 199 in Dublin to "take up a pilot project and see how we work with young people.
"We just have to start and see. If it works, it works. If it doesn't work, we start again."
Dr Martin was speaking to reporters after confirmation mass at St Mary's Pro-Cathedral in the wake of yesterday’s Yes vote.
He said: "The Church has to find a new language which will be understood and heard by people.
"We have to see how is it that the Church's teaching on marriage and family is not being received even within its own flock.
He also said he could never see gay marriages taking place in Catholic churches.
"Because for the Catholic Church there's a very strong sentiment that marriage is something between a man and a woman."
