Taoiseach Enda Kenny does not want the country "convulsed" over the abortion issue as it was in the 1980s.
But Mr Kenny said any further developments in terms of changing the laws governing abortion will be a matter for the next Government.
"I would see an environment for a national, compassionate discussion. I do not want the country convulsed like it was in the 1980s for a period of years with arguments for and against this very sensitive issue," Mr Kenny said.
He was speaking after Independent TD Clare Daly's abortion bill, which proposed allowing terminations in cases of fatal foetal abnormalities, was comfortably defeated by 104-20 votes in the Dail.
"These are all very sensitive issues, personal tragic cases ... (but) the bill presented to the Dail was unconstitutional," the Taoiseach said at an event in Croke Park yesterday.
He said that the Government can only deal with matters that are constitutional.
"There are a number of very sensitive issues that cannot be treated glibly. These are all personal, sensitive, tragic cases," Mr Kenny said.
"The bill presented to the Dáil was unconstitutional. For that reason, the constitution says legislators can only vote on issues that are constitutional and this clearly was not."
The 1983 constitutional amendment gave equal status to both the mother and the unborn. This was the main legal barrier to the Government supporting Ms Daly's bill.
Mr Kenny said abortion only applies in Ireland when there is a threat to the life of the mother.
He also said issues surrounding abortion "cannot be treated glibly, that cannot be treated as a matter of fact - as if you can change the Constitution like that".
Issues surrounding fatal foetal abnormalities, and pregnancies in cases of rape or incest, are very sensitive and controversial ones, he said.
However he added: "They must be dealt with in the future.
"We have already made it clear that this is a matter for the next government."
Labour lost one of its TDs after Anne Ferris voted against the Government on the issue on Tuesday evening.
Ms Ferris was one of several TDs who yesterday pleaded for a free vote on the bill proposed by Ms Daly, a left-wing opponent of Labour.
Labour leader Joan Burton was forced to deny that the events of the week had "shaken" her leadership.
And Labour backbencher Michael McNamara pledged to bring his own bill on the issue of fatal foetal abnormalities to the Dáil - keeping the divisive issue on the radar of TDs and senators.