Northern Ireland is the only part of the UK and Ireland where termination is restricted to cases where there is a threat to a woman's life or serious risk to her physical or mental health,
following last month's referendum in the South.
The High Court ruled in 2015 that Northern Ireland's abortion laws violated human rights law.
However, Northern Ireland's attorney general and department of justice challenged the decision and won on appeal.
In 2017 the Court of Appeal ruled that even if that was the case, the law falls under powers devolved to Stormont and cannot be changed in Westminster.
Les Allamby, chief commissioner at the Northern Ireland Human Rights Commission, said: "If the court rules that there is a violation of human rights, then that becomes a very serious issue for the UK government.
"In the absence of the Northern Ireland Executive and Assembly, it becomes a human rights issue, not simply a matter of policy that’s devolved to Northern Ireland."
Dawn McEvoy from the Both Lives Matter campaign said: "Abortion campaigners are using these very extreme and difficult circumstances to try and instigate a situation where there is unlimited access to abortion, decriminalisation of abortion."
