Minister for Children and Youth Affairs James Reilly has reiterated the Government has decided not to hold any further referendums during its term of office.
Mr Reilly made the remarks in the wake of calls from Tánaiste Joan Burton and other Labour TDs for a repeal of the Eighth Amendment.
Minister of State for Primary and Social Care Kathleen Lynch earlier said repealing the amendment should be "do-able" after the same-sex marriage referendum was passed.
Speaking on RTÉ's Morning Ireland, Ms Lynch said changing abortion laws in the Constitution would allow the Government to legislate in a practical and reasonable fashion for women who find themselves in particular circumstances.
She said it is important that the repeal happens so the Government can deal with fatal-foetal abnormalities.
"No-one would have believed when we were drawing up the programme for Government that we would be in the position we are in now in relation to marriage.
"I believe that if you are forceful enough in your conviction, which I think we are, that repeal of the eighth amendment is very do-able.
Responding to the remarks, Mr Reilly said he believed "we have to address this issue around fatal foetal anomalies as a priority, but we have also to address it in a manner that does not deliver abortion-on-demand because I do not believe the Irish people want that."
Earlier, Mr Reilly said during the passage of the Protection of Life During Pregnancy Bill he told the Dáil he had got very clear advice from the Attorney General that, in order to address the issue of fatal foetal anomalies in particular, a referendum would be required.
He added that he would be working strongly for and towards that, but that the current Fine Gael-Labour administration had already decided it would not be holding further referendums.
Asked for his view on access to abortion in Ireland in cases of rape and incest, which Labour favours, Mr Reilly said "these are all issues to be addressed by the Fine Gael party as the (general election) manifesto is being put together and a new government is being formed whenever that might be".
"There are very complex issues here," he said "and there are a lot of diverse views within the political system and within Fine Gael," he added.
The Eighth Amendment of the Constitution was enacted in 1983. It states: "The State acknowledges the right to life of the unborn and, with due regard to the equal right to life of the mother, guarantees in its laws to respect, and, as far as practicable, by its laws to defend and vindicate that right."
It is referred to as Article 40.3.3 of the Constitution and was introduced after a referendum.