Mr. Varadkar’s party, the center-right Fine Gael, does not have a majority in Parliament; it depends on five independent lawmakers and a pact with its main rival, the socially more conservative Fianna Fail. A poll published by The Irish Times on Friday showed that a majority of lawmakers in both houses support repealing the constitutional ban. In the lower house, or Dail, 82 lawmakers said they would vote yes, and 40 no, with 36 undeclared. In the upper house, the Senate, 31 said they supported removing the ban, 11 oppose it and 17 are undeclared.

Early public opinion polls suggest that a majority of Irish voters would favor removing the constitutional ban in a referendum. A poll published in The Sunday Business Post this weekend showed 60 percent support for repeal, though support for unrestricted abortion up to 12 weeks was weaker, at 51 percent.

In view of this, and the continuing opposition to abortion within the larger conservative parties, it is not certain that a bill allowing unrestricted abortion up to 12 weeks would be approved by Parliament.

Unrestricted abortion has always been illegal in modern Ireland, although terminations were sometimes carried out in hospitals when considered necessary to save the mother’s life. In 1981, however, the Pro-Life Amendment Campaign, a lay group backed by the Roman Catholic Church, began lobbying for a constitutional amendment that would prevent terminations on any grounds.

A 1983 referendum on such an amendment passed with 67 percent of the vote, despite warnings from some constitutional and medical experts that the resulting ban would create difficult legal and medical situations.

One such affair — known as “The X Case” — emerged in 1992, when the then-attorney general secured a court order to prevent a 14-year-old rape victim, identified only as “X,” from leaving the country to obtain an abortion in England, the most common destination for Irish women seeking terminations. Ireland’s Supreme Court overturned the decision, reinterpreting the constitutional ban as allowing terminations in cases where pregnancy threatened a woman’s life. The teenager had expressed a wish to kill herself rather than carry the baby to term.

Anti-abortion campaigners went on to lobby for two further referendums to exclude a suicide risk as a reason to allow abortion, but — in a sign of changing attitudes — were defeated both times.