The Love Both campaign, which is seeking to retain the Eighth Amendment in the Constitution, has called on the Minister for Health to debate the issue of abortion with one of its representatives.
The challenge came at a press conference this afternoon, when the group highlighted the need for perinatal and palliative care facilities, to help families of babies with life-limiting conditions, instead of introducing abortion.
Spokesperson Sinead Slattery said no Government-sponsored debate has taken place in the last six years focused on positive alternatives to abortion.
Earlier, Minister for Health Simon Harris questioned the proposals of those campaigning for a No vote in dealing with victims of rape or incest, those taking abortion pills or travelling for abortions.
He said there was also a duty on those saying that the status quo is fine to explain why.
Today, Love Both said that while hundreds of Irish couples are on waiting lists having been declare suitable to adopt a child, just five infants were presented for adoption in 2016.
A spokesperson for the minister said Mr Harris will continue to argue the case for change in Ireland.
She added that the scheduling and composition of debates is a matter for broadcasters to determine, but that the minister looks forward to participating.
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Meanwhile, Mr Harris has said it is far too easy for men to think that the referendum is not an issue that affects them.
Mr Harris was joined by members of the Fine Gael party, including senior ministers, who canvassed for a Yes vote in Dublin city centre this morning.
Minister for Education Richard Bruton said while men may be inclined to "opt out" of the debate because they feel it does not involve them, he advised men to take a keen interest in the upcoming referendum.
Meanwhile the Minister for Justice said that looking back over the last 35 years, it was fair and reasonable to say that the Eighth Amendment had not served society well.
Charlie Flanagan said it had served Irish women particularly badly.