* Voters to be asked to hand parliament right to legislate
* Abortion with no restrictions to 12 weeks may follow
* Opinion polls suggest clear majority in favour of change
* Catholic Church has lost much influence in Ireland (Adds detail, quotes, latest polling)
By Padraic Halpin and Graham Fahy
DUBLIN, March 28 (Reuters) - Ireland will hold a referendum on May 25 on whether or not to liberalise its abortion law, the first opportunity in 35 years to overhaul one of the world's strictest regimes that has long divided the once deeply Catholic nation.
A complete ban on abortion was only lifted five years ago for cases where the mother's life was in danger. That move fuelled calls to give voters under the age of 50 their first say on more comprehensive reform.
Voters will be asked if they wish to repeal an amendment to the constitution that was inserted following a 1983 referendum to enshrine the equal right to life of the mother and her unborn child, and to instead enable parliament to set the laws.
"After weeks and months of politicians debating the issue, now the people of Ireland get the chance to have their say," Health Minister Simon Harris said after the date was announced.
"My message is if you can no longer accept thousands of women every year going abroad to access terminations, this is your time to right that wrong," said Harris, who will campaign for a change in the law.
The Roman Catholic Church's once blanket influence on politics and society in Ireland has plummeted in recent years following a series of clerical sex abuse scandals.
The referendum will be held three months before Pope Francis makes the first papal trip in nearly 40 years to a very different Ireland.
The government began in January the process of setting a date with the aim of holding the referendum before the end of May so that students can vote before many leave to spend the summer months travelling or working overseas.
Polls have shown a sharp generational divide, with younger voters far more like to back change and a clear majority over the age of 65 opposed.
The most recent poll on Sunday showed a slight drop in support for a 'Yes' vote to 56 percent from 60 percent two months ago, with 26 percent opposed and 18 percent undecided.
Ireland's two main political parties are also divided. Prime Minister Leo Varadkar will campaign for reform, but some in his Fine Gael party take a different view, while the main opposition, Fianna Fail, is split even deeper despite its leader supporting a change in the law.
Canvassing of votes has already begun. More than 10,000 "pro-life" campaigners rallied in Dublin this month to oppose the referendum while "pro-choice" advocates hope to tap into the support that saw Ireland become the first country in the world to back gay marriage in a referendum in 2015.
If voters back the proposed changes in the abortion referendum, the battle will move to parliament, where the government plans to introduce legislation for terminations with no restrictions to be allowed up to 12 weeks into a pregnancy.
However, with politicians further split on what comes next and Fine Gael and Fianna Fail allowing members a free vote, Varadkar cannot guarantee voters that his minority government will be able to legislate for such access. (Reporting by Graham Fahy Editing by Padraic Halpin and Gareth Jones)
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