Pro-choice groups have launched a campaign calling for a referendum to change limited laws on abortion.
Thirty years since the eighth amendment was signed into the Constitution - giving the unborn equal right to life to a woman - the campaigners want it removed from law.
Action on X spokeswoman Ailbhe Smyth said she was confident the Constitutional Convention would be willing to debate the contentious issue - given its recent liberal stance on same-sex marriage.
"The Constitutional Convention has proved itself to be quite open and has made a number of somewhat surprising recommendations on issues which might have been considered contentious in the first instance," Ms Smyth said.
"Perhaps today is not the very best day to be mentioning the word 'referendum', but that seems to be the way the cookie crumbles and there we have it."
The National Women's Council of Ireland submitted a formal request asking the Constitutional Convention to review Article 40.3.3 with a view to removing it.
Council spokeswoman Jacqueline Healy, along with the other women's rights and civic groups, claimed existing legislation on abortion does not go far enough in protecting women.
The Protection of Life During Pregnancy Act 2013, which was signed into law in the summer, allows for abortion when there is a real and substantial risk to a woman's life - including the threat of suicide.
But it still prohibits termination in cases of rape, incest, inevitable miscarriage and fatal foetal abnormality.
The campaigners have argued the law also ignores the needs of women who decide that having an abortion is in their best interest.
It also criminalises women and people who support them, including their doctors, if they have an abortion in Ireland.
"Only a referendum can sufficiently protect the lives and health of women and girls," Ms Healy said.
"The new legislation on abortion only deals with a tiny number of cases and will not change anything for the majority of women with crisis pregnancies in this country."
The Constitutional Convention voted overwhelmingly in favour of changing the Constitution to allow same-sex marriage.
The vote in April prompted the Government to commit to holding a referendum on extending marriage rights, which could happen as soon as 2014.
Other issues debated by the convention have included women in politics, the presidential term, a reduction in voter age and voting rights for citizens abroad.
A spokesman for the convention said it will consider requests for issues to debate following the next meeting, when members will discuss the country's laws on blasphemy.