Taoiseach Enda Kenny has said that any further developments in terms of changing the laws governing abortion will be a matter for the next Government.
Speaking in Dublin, he said he does not want Ireland "convulsed" over abortion like it was in the 1980s.
Mr Kenny said Independent TD Clare Daly's bill for abortion in cases of fatal foetal abnormalities was unconstitutional.
He said these "are all personal, sensitive, tragic cases".
Mr Kenny also said issues surrounding abortion "cannot be treated glibly".
He said: "The bill presented to the Dáil was unconstitutional and for that reason the Constitution says that legislators can only vote on issues that are constitutional. This one clearly was not".
The Taoiseach said lawful terminations in Ireland only apply in cases where there is a threat to the life of the mother.
"Fatal foetal abnormalities, the consequences of pregnancy from rape or incest are very sensitive issues and they're very controversial issues and they must be dealt with in the future".
Mr Kenny said the Government has made it clear that "this is a matter for the next government" and sees a "requirement for a rational, understanding, sensitive discussion".
He added: "I do not want the country convulsed like it was in the 1980s, for a number of years, with arguments for and against in these very sensitive issues".
Ms Daly's Fatal Foetal Abnormality Private Members' Bill was defeated in the Dáil yesterday.
She moved a bill to allow terminations in cases where the foetus will not survive outside the womb.
Former justice minister Alan Shatter has said that he hopes whatever parties that compose the next government will agree that a referendum is held on abortion, within the life-time of that government.
Speaking on RTÉ's News At One, he said it is no secret that he is of the view that the Eighth Amendment was a mistake and that a woman should not be compelled to maintain a pregnancy if a victim of rape.