The Government is facing fresh calls for a referendum to repeal the 8th amendment.
A Millward Brown opinion poll in today's Sunday Independent found 63% of people support the right to abortion in cases of fatal foetal abnormality.
The poll also found that 60% say abortion should be allowed in the case where the mother is suicidal.
The 8th Amendment of the Constitution gives the unborn child equal rights to the mother and outlaws abortion.
Orla O'Connor, director of the National Women's Council of Ireland said: "The poll clearly shows that the majority of Irish people want to see abortion in certain circumstances, and that means there has to be a referendum, and this is what the National Women's Council have been calling on the Government to put in place.
"There needs to be a referendum to remove the 8th Amendment.
"The poll is showing that Irish people are well ahead of politicians, and there needs to be leadership shown by the Government on the issue of abortion."