Fine Gael TDs opposed to the abortion legislation want to be able to repeal the law - if the number of pregnancy terminations rises from the current rate of 20 to 30 per year.
According to The Sunday Times, Cork North West TD Michael Creed raised the proposal with the Taoiseach last month, and has the support of a group of his party colleagues.
They want to see the Bill brought back to the Dáil once a year - where it could be scrapped if the number of abortions rises significantly.
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However, Labour ministers are said to be strongly opposed to any changes to the legislation.