Yes Equality have asked Archbishop Eamon Martin to debate the Marriage Equality referendum, after he released a statement saying clerics "cannot support" it.
The Primate of the Roman Catholic Church in Ireland said he issued the statement following requests for clarity on the church's position on the vote.
Part of his statement said clerics "cannot support an amendment to the Constitution which redefines marriage and effectively places the union of two men, or two women, on a par with the marriage relationship between a husband and wife which is open to the procreation of children."
Grainne Healy, spokesperson for Yes Equality, said: "We have always respected the right of the Catholic Church Hierarchy to express its views.
"We note the lengthy statement issued by Archbishop Eamon Martin this evening. We disagree with much of its content and are disappointed with its tone. While it is directed at church goers, it raises many questions for those of us actively engaged in issues surrounding equality.
"Now that the referendum campaign is underway, and in light of his statement, we invite Archbishop Eamon Martin to discuss with us the issues he raises surrounding the Marriage Equality Referendum in any public or media forum.
"A core element of the Yes Equality has been having conversations with people all across Ireland; people of all ages and of all beliefs and none. We will continue these conversations, to listen to and talk with people up to Polling day."