A clear majority of Irish people would vote in favour of liberalising abortion laws and allowing terminations on request up to 12 weeks, according to a poll released as the cabinet prepares to meet to hammer out details of a referendum on the issue.

In response to the question “Will you vote to change the constitution so that the government can legislate for abortion up to 12 weeks, or will you vote not to change the constitution?”, 56% said they would vote in favour, 29% said they would vote against, and 15% said they did not know or offered no opinion.

Changing the constitution would mean repealing Ireland’s eighth amendment, which recognises the equal rights to life of a foetus and the mother during pregnancy and in effect bans abortion in almost all circumstances.

Pro-choice campaigners say the amendment, added to the constitution after a referendum in 1983, creates a legal “chill factor” in the health system, even in cases where Irish law allows for a ­termination, such as when a pregnancy would result in the mother’s death.

The responses to the Irish Times/MRBI opinion poll suggest a significant swing towards the repeal side. When asked if their view on abortion being more widely available had changed in the last year, 19% of respondents said they were more open to the idea, while 3% said they had become less open.

The Irish prime minister, Leo Varadkar, under pressure in recent weeks to state his position on abortion, has said he will do so before a special meeting of the cabinet on Monday night. It is expected the meeting will give the go-ahead for a referendum later this year, with May being suggested as the preferred time for the vote.

Varadkar’s Fine Gael party and the main opposition party, Fianna Fáil, are divided on the issue. Generally speaking, MPs from more rural, conservative constituencies are opposed to reforming the law, while those in urban areas are more likely to be in favour.

Micheál Martin, Fianna Fáil’s leader, shocked many in his party last week when he came out openly in favour of a yes vote to repeal the eighth amendment and allow for limited abortions.

A large group of Fianna Fáil MPs who oppose liberalising abortion laws are trying to prevent the referendum being held in May, which they argue would benefit the pro-choice side because it would be easier for students to vote in big cities.

Quick Guide Ireland's political parties Show Fine Gael Forged in the Irish civil war as the side that accepted the Anglo-Irish Treaty of 1921, Fine Gael has a centre-right, pro-market and pro-European outlook. The party has two distinctive wings: a socially liberal, urban and professional base, and a rural grassroots following with strong links to the farming community. Fianna Fáil Initially comprising opponents of the Anglo-Irish treaty, Fianna Fáil is also seen as centre right. It dominated Irish politics for much of the 20th century and used to enjoy a predominantly working-class membership. An archetypal pragmatic political force, the party now has strong links to builders and property investors. Sinn Féin Once umbilically linked to the Provisional IRA, Sinn Féin has benefited enormously from the Irish peace process, with Gerry Adams and Martin McGuinness becoming internationally renowned political figures. The party takes a populist and pragmatic approach to economic issues. Photograph: Niall Carson/PA

There is a generational angle to the debate: support among 18- to 24-year-olds in the poll was 74%, while among those over 65 it was 36%.

While the country remains overwhelmingly Catholic, public opinion has become far more socially liberal in recent years. A complete ban on abortion was only lifted in 2013 to allow terminations in cases where the mother’s life was in danger.

The abortion debate has become increasingly heated and acrimonious in recent months. This week, the charity Down Syndrome Ireland criticised the anti-abortion Love Both group over leaflets it had distributed with the headline “90% of babies diagnosed with Down syndrome in Britain are aborted”.

“This is very disrespectful to both children and adults with Down syndrome and their families,” the charity said. “It is also causing a lot of stress to parents. People with Down syndrome should not be used as an argument for either side of this debate.”

Meanwhile, the Methodist church in Ireland has become the latest of the four main Christian denominations in the Republic to oppose the proposed abortion reforms. A statement from the Methodist Council on Social Responsibility said the church had “consistently been against abortion on demand”.