Ireland is still deeply divided over the issue.
A recent poll by Ipsos/MRBI found 67 percent of respondents were opposed to abortion in general but that 76 percent were in favor of legalizing it cases of rape.
Varadkar, who trained as a doctor, has called the current laws “too restrictive.”
Varadkar has said he would support abortion in cases of fatal foetal abnormalities but is not supporting wider liberalization.
Thousands of Irish women currently travel abroad for abortions every year, mainly to England.
A “March for Choice” took place in London outside the Irish embassy on Saturday.
The upcoming vote has rallied those on both sides of the debate, including activists seeking to keep the current legislation in place.
In central Dublin, a small number of activists opposed to abortion handed out leaflets on Saturday, something they intend to do every week from now on.
“The country is very polarized at the moment, so what we try to do now is to reach people on the fence, who haven’t made up their minds yet,” said organizer Alan Keena.
The Irish government has already sought to gauge public opinion, setting up a Citizens’ Assembly which between November and April debated the eighth amendment.
Summing up their discussions, a majority of the 99 members recommended legalizing abortion in a wide range of circumstances.
A parliamentary committee has also been examining the abortion law, but on both sides of the debate there is mistrust of officials’ approach.
“The wording of the referendum will have a large bearing on the outcome and my instinct is that there will be compromise, there has to be, because there are 22 people from all sides on that committee,” said Anna McKenna, 66, a retired teacher on Saturday’s march.
Although the pro-abortion camp reacted positively to the referendum announcement, there is suspicion that MPs continue to be heavily influenced by the church in the mainly Catholic country.
Unlike the referendum which saw Ireland vote in favor of same-sex marriage in May 2015, no politicians have yet taken a strong position calling for greater abortion access.
Irish media has reacted similarly, reluctant to take a bold stance on an issue which has divided Irish society.