Speaking in the Dáil today, Minister for Health Simon Harris called the job of legislating for abortion "serious and challenging".
The government introduced legislation yesterday to allow for a referendum on repealing the Eighth Amendment and published a policy paper detailing plans to allow abortion up to twelve weeks' gestation.
"We will not be able to address issues in relation to women who have had fatal fetal abnormalities in their pregnancy, in relation to women and girls who have been raped and abused in this country, to the fact that our daughters, sisters, wives, mothers, work colleagues could be using the abortion pill without medical supervision", Harris said.
Saturday's rally follows on the heels of a march by abortion rights protesters on Thursday, marking International Women's Day-the same day cabinet passed a bill making it possible for the referendum to go ahead.
The bill lays out the framework for the referendum, which will ask people whether they want to retain the Eighth Amendment or delete it from the Constitution and insert the following wording: "That provision may be made by law for the regulation of termination of pregnancy".
Mr Harris also said he was looking into introducing a system of free contraception in an effort to reduce pregnancies. "Retaining the Eighth Amendment will not prevent it from happening".
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Update - 1.48pm: After the Cabinet meeting, Leo Varadkar said: "On my first day as Taoiseach I committed to holding a referendum this year".
Providing access to medical abortion on request in early pregnancy, and in later pregnancy in additional circumstances, is the minimum needed to respect and fulfil women's human rights.
The decision comes just days after Ireland's Supreme Court ruled that the unborn child has no constitutional rights other than the right to life, a decision pro-lifers say highlights the importance of defeating the referendum.
Ailbhe Smyth of the Coalition to Repeal the Eighth Amendment said: "This is a historic and momentous day for Ireland, and for the women of Ireland in particular".
The decision cleared the way for the referendum in a country where terminations are only allowed when the life of the mother is at risk.
"It's about trusting women to decide, in the early weeks of their pregnancy, what's right for them and their families", Varadkar said.