Around 80pc of voters said they would support legislation to allow for abortion in cases where the mother's life was in danger.
The Behaviour and Attitudes poll for the 'Sunday Times' found that 14pc of the 923 voters polled were opposed to such legislation, and 6pc had no opinion.
But several Fine Gael and Labour TDs contacted yesterday said they did not want to comment until an expert group reported, due to the sensitivity of the issue.
One TD described how he had got 500 responses on his Facebook page after he made a previous comment about abortion.
Labour Junior Minister for Primary Care Roisin Shorthall said there was a need to wait for the expert group's report.
Difficult
"It's a difficult issue, and there is a wide spectrum of views in all parties in relation to it. So it's a matter of taking a sensible approach to it," she said.
Many Labour TDs are in favour of acting on the 1992 Supreme Court ruling on the X case on a suicidal teenager who had become pregnant after being raped by a neighbour.
The court stated that abortion was permissible where a mother's life was at risk, including from suicide.
But successive governments have not introduced legislation to give effect to this judgment.
Many Fine Gael TDs are opposed to any such legislation.
The expert group is due to present a report to Health Minister James Reilly this month, who will then bring it to Cabinet.