Catholics for Choices welcomed a decision by two-thirds of voters to repeal the state constitution's Eight Amendment - legislation which prohibits terminations unless a mother's life is at risk.
President, Jon O'Brien said: "The 'yes' vote to repeal the eighth was a historic step for Ireland and women's rights and dignity.
"As a Dubliner from Drimnagh, I came of age in an Ireland where the heavy hand of the Catholic hierarchy kept women from taking control over their bodies and their lives.
"This victory shows the Irish nation is at peace with its Catholic identity and its prochoice position.
"Now, it is simply up to the politicians to do their jobs and bring this vote into legislative reality."
Ministers previously indicated that they would follow a 'yes' vote by aiming to introduce more relaxed abortion laws by the end of the year.
The Irish Government expressed support for allowing women to end a pregnancy within the first twelve weeks, subject to medical advice and a cooling-off period.
It also backed terminations being allowed between twelve and 24 weeks in exceptional circumstances.
The proposals met resistance from the four main Christian denominations in Ireland - The Catholic Church, the Presbyterian Church in Ireland, the Church in Ireland (Anglican) and the Methodist Church.
The Presbyterian Church in Ireland said on Saturday - as the result of Friday's referendum was confirmed - that the day was "not a day for celebration, but for quiet reflection".
Moderator, Rt Rev Dr Noble McNeely said: "We acknowledge the outcome of yesterday's referendum with a profound sense of sadness.
"The country is evidently living through a defining moment in which the inherent value placed on human life is at stake.
"We would strongly urge the Government and the Oireachtas (Irish parliament), as they legislate, to keep the promise they have made to the electorate to make abortions 'rare' in Ireland, and to ensure that the unborn with disabilities, like Down's syndrome, will not have their lives terminated.
Meanwhile, the Catholic Archbishop of Armagh Eamon Martin wrote on Twitter: "Every human life remains beautiful, every human life remains precious. Every human life remains sacred."
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