The Fine Gael TD said he believes the issue of fatal foetal abnormalities needs to be addressed, as well as in cases of rape, incest and when the health of a mother is at risk.
Deputy Griffin said that while he believes a referendum needs to be held, an awful lot needs to be done before we get to that point.
He was one of 67 Fine Gael TDs surveyed by the Irish Independent on the issue. 30 of those surveyed said they were undecided or wouldn’t give a position, 15 supported change and 7 opposed it.
Minister Jimmy Deenihan was one of 15 TDs who did not respond to the paper on the issue.