A group campaigning for a 'No' vote in the Marriage Equality Referendum is calling on the Taoiseach to take part in a live debate on the issue.
Enda Kenny appears to be ruling out taking part in a live debate, saying there is no other political party leader on the 'No' side to debate him.
Mr Kenny says the campaign is not a party political one and so there is nobody to oppose him in it.
He said: "I've no intention of turning it into a party political debate, it's not that kind of referendum. If people turn it into a party political debate, there is no party that is opposed to this measure, so it's a case of constantly engaging with groups and communities.
"And what they are doing is deliberately involving issues that they know are not central to the question."
Mothers and Fathers Matter said the Taoiseach’s refusal to debate the issue is "pathetic".
Mothers and Fathers Matter issued a statement saying: "In four weeks, people across the country are being asked to go to the polls and vote on a proposal brought forward by the Taoiseach.
"In January, Mr Kenny said he would be “happy to debate” this proposal live on air with opponents.
"When he made that promise, he knew full well that there would not be “party political” opposition to the referendum, so for him to try and use that excuse now to avoid a debate reeks of a naturally occurring form of fertilizer.
"Does he really think people will believe that there's nobody good enough to debate him? It's a real insult to 'Yes' side spinmeisters that they have to sell this nonsense for the next few weeks.
Mothers and Fathers Matter said that they are ready for a debate whenever the Taoiseach is.
They said: "Evidently, in the intervening period, someone in Government buildings has decided that the leader of the country can’t be trusted to defend his own ideas when challenged.
"The Irish people are being presented with a dishonest campaign that says marriage has nothing to do with children, a campaign that says motherhood and fatherhood don’t matter, and a campaign that says that the family in the constitution can mean anything that the government wants it to mean.
"That the Taoiseach can’t be trusted by his own staff to defend these ideas should tell voters everything they need to know."
The referendum will be held on May 22, with the deadline for registering to vote on May 5. You can find more information on how to register here.