MPs voted 383 votes to 73 in favour of same-sex marriage and 332 to 99 on the abortion amendment.
The amendments were attached to the Northern Ireland (Executive Formation) Bill, which aimed to help return powersharing to Northern Ireland, and were put forward by MPs Stella Creasy and Conor McGinn.
The Presbyterian Church in Ireland has expressed its disappointment and regret following the votes on Tuesday, saying it was: "paving the way for liberalisation of abortion law and the introduction of same-sex marriage in Northern Ireland."
It has called on the Government to clarify how it will respond to the amendments in terms of their implementation and what consultation will be undertaken within the timeframe.
The Church of Ireland's Rt Revd Dr Kenneth Kearon, Bishop of Limerick and Killaloe, said before the votes: "While the absence of an Assembly is very regrettable, it is equally regrettable that MPs at Westminster are seeking to use the opportunity to introduce Northern Ireland-specific legislation on two of the most controversial issues facing the Province today."
Regarding abortion he said: "The tradition of the Church of Ireland would reject an unrestricted access to abortion, while being concerned to ensure provision for hopefully rare circumstances and in a secure medical setting. Where individuals draw such a line will inevitably differ. Instances where the life of the woman is at serious risk have long been regarded within Church of Ireland teaching as situations where termination of a pregnancy would be justifiable."
"With respect to same-sex relationships, we have stated that 'the Church of Ireland defines marriage as between a man and a woman. The church has often existed, in history, with different views from those adopted by the state, and has sought to live with both conviction and good relationships with the civil authorities and communities in which it is set."
Other church leaders gave their feelings before the votes.
A spokesperson for Pro-life group Right To Life UK, Clare McCarthy said: "This amendment is an unconstitutional and disrespectful attempt to override devolution in Northern Ireland and to attempt to impose abortion on demand on the Northern Irish people. The law on this issue should be a decision for the people of Northern Ireland and their elected representatives, not for MPs in Westminster to decide.
"It is totally constitutionally inappropriate to bring forward abortion amendments to a Bill which has nothing to do with abortion in any way, to legislate on such a sensitive matter. Any imposition of abortion law on Northern Ireland from Westminster would undermine devolution and the Good Friday Agreement.
"No consultation on this amendment was possible. The people of Northern Ireland had next to no opportunity to voice their opinions.
"Westminster must respect the principle and spirit of devolution and ensure the people of Northern Ireland, through their elected representatives, get to decide on what law and policy should apply in that jurisdiction."
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