Leo Varadkar says the government has no mandate to hold a referendum on whether the current system can be relaxed.
But he says he will be asking Fine Gael to campaign for one in the next election, to allow abortion in cases of fatal foetal abnormality.
However independent TD Mick Wallace says the minister's excuse for delaying the referendum doesn't hold up:
“Your argument, Minister, that you don’t have a mandate to challenge the eighth amendment, is horseshit,” Mr Wallace said.
“You didn’t have a mandate to bring in the property tax, you didn’t have a mandate to pay the unsecured bondholders.”
But Leo Varadkar has ruled out any further laws or referendums on abortion in the lifetime of the current Dáil.
He is rejecting a bill from Clare Daly, to allow abortion in cases of fatal foetal abnormality, because he says it is in breach of the Constitution.
But he says that Constitution should be changed, and he wants Fine Gael to deal with it in the next government.
Meanwhile the Dáil was told earlier that Ireland is failing its women who are pregnant with fetuses which have fatal abnormalities.
Clare Daly is urging the government to accept her bill which would allow abortion in those circumstances, as long as two doctors approve.
The government says the bill is unconstitutional - but it is believed that up to half of the Labour parliamentary party want it passed anyway.
Officially the government opposes the bill, but internally it is believed Labour is facing huge disquiet - with up to half of its members hoping to support it.
Those members believe the party will lose its traditional liberal support if it blocks this bill, especially when it is been written by legal experts and should not have any unexpected ramifications.
The bill will not pass one way or another, as Sinn Fein will abstain and Fianna Fáil will give a free vote.
But some in Labour also want a free vote - something other members see as a slippery slope with an election on the horizon.
Clare Daly said the state is failing vulnerable women if it does not address their problems.
These parents have pleaded with TDs to vote in favour of the amendment:
