It adds that the bill "has the capacity to undermine the delicate political calibration between Northern Ireland and Westminster and to cause significant damage to attempts to restore the Northern Ireland Assembly."
O'Loan and Eames called on the government to withdraw the Northern Ireland (Executive Formation) Bill.
Failing this, they called for an amendment they introduced which would require public consultation and the support of a majority of members of the Northern Ireland Assembly before any change in the region's legislation.
Bills to legalize abortion in cases of fatal fetal abnormality, rape, or incest failed in the Northern Ireland Assembly in 2016.
Both amendments to the were introduced by Labour MPs.
Stella Creasy, who represents a London constituency and who introduced the abortion amendment, has said the Commons "spoke clearly to say we wouldn't accept the rights of women in Northern Ireland being ignored any longer".
Earlier this year Creasy intended to propose an amendment to a draft Domestic Abuse Bill that would give the British parliament jurisdiction over abortion laws throughout the United Kingdom. However, the bill's scope was restricted to England and Wales by the Conservative government.
She also introduced an amendment to the Northern Ireland (Executive Formation and Exercise of Functions) Act 2018 to repeal Northern Irish law on abortion and gay marriage, which was defeated.
Ahead of last week's vote in the Commons, Archbishop Eamon Martin of Armagh registered his deep concern that the bill would be hijacked "to remove existing legal protection for unborn babies and to 'fast track' the legalisation of abortion on demand in Northern Ireland. How tragic it is for humanity that some legislators would 'fast track' the ending of the lives of the most defenceless in our society."
Abortion and same-sex marriage are both legal in both the United Kingdom and the Republic of Ireland. Elective abortion is legal in the rest of the United Kingdom up to 24 weeks, while currently it is legally permitted in Northern Ireland only if the mother's life is at risk or if there is risk of permanent, serious damage to her mental or physical health.
Northern Irish women have been able to procure free National Health Service abortions in England, Scotland, and Wales since November 2017.
(Story continues below)
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In June 2018, the Northern Ireland Human Rights Commission challenged the region's abortion laws in the UK Supreme Court. While the Supreme Court concluded that Northern Ireland's abortion laws violated human rights law by banning abortion in cases of fatal fetal abnormality, rape, and incest, it threw out the case saying it had not been brought forward by a person who had been wrongfully harmed by the law.