But it seems that less liberal attitudes came into play in other circumstances.
More than three quarters of Irish citizens are in favour of allowing abortion where continuing the pregnancy could damage the woman's health.
A survey has revealed that 77% of people polled backed a termination in such cases.
It also showed that 75% supported abortion where there is a foetal abnormality which will result in death prior to or shortly after birth.
And 73% of those quizzed backed allowing terminations in cases of rape.
But less liberal attitudes prevail in other circumstances.
It showed that 58% opposed allowing termination where a parent or parents would have difficulty supporting the child, with 30% in favour.
A total of 60% were against abortion on unrestricted grounds, but views were not sought on term limits.
The findings also showed stronger pro-choice attitudes among younger adults.
And the 40% of 18 to 34-year-olds approved of abortion if parents would have troublesupporting a baby, compared to 20% of over-55s.
One in three urban dwellers favoured termination in these cases, compared to 24% in rural areas, the Sunday Times poll found.
The Citizens’ Assembly last month came out in favour of liberalising the circumstances in which abortion can be obtained in Ireland.
A referendum is expected in 2018.
Amnesty Ireland executive director Colm O’Gorman said: “The Citizens’ Assembly spent five months looking at this issue.
“They came to this ‘upon request’ model in early pregnancy on the basis that this was the most reasonable and considered way to provide access in cases of pregnancy resulting from rape and where there was a risk to the woman’s health.”
Senator Ronan Mullen said the poll shows people do not favour abortion on demand, but warned allowing the procedure in certain cases is problematic.
He added: “People are under-informed about the consequences of some of these choices.
“It is difficult to know whether a child is going to die shortly after birth or not. The British law on ‘health grounds’ is very difficult on paper, very liberal on practice.”
The Pro Life Campaign said it is confident surveys showing support for abortion would change dramatically in the event of a referendum.
The group was responding to yesterday’s poll which claims 75% of the public support abortion on the grounds of the mother’s health being in danger.
PLC spokeswoman Cora Sherlock said: “Those who support abortion on request will of course try to come forward with a proposal that appears restrictive but in reality would be nothing of the sort.
“You only have to look at what has happened in other countries to know that this is an inescapable fact. As a society, we either protect all human life or you end up protecting none.”