If their proposal becomes law, the Stopes Clinic, which opened in Belfast in October, would be unable to offer abortions, The Irish Times reported.
Abortion is only legal in Northern Ireland if continuing a pregnancy would be a great risk to a woman's physical or mental health. Fewer than 50 are carried out in the province every year.
Caitriona Ruane, a Sinn Fein legislator, said the republican party opposes the amendment because it would limit women's rights to obtain medically necessary abortions.
The Stopes Clinic, named after British birth control pioneer Marie Stopes, is the only private clinic in Ireland offering abortion.
Abortion is currently a controversial issue on both sides of the border. In the Republic of Ireland, where a woman died last year when doctors at a Galway hospital refused to end her pregnancy after she went into premature labor, officials are debating clarifying the law that permits abortion only when a woman's life is at risk.
In Northern Ireland, the Department of Health has said it will release proposed changes to abortion guidelines next week.