A spokesman for the country's Catholic bishops has expressed surprise at Taoiseach Enda Kenny's comments on same-sex marriage yesterday.
Mr Kenny told RTÉ News that it was a matter for the church to determine whether or not to continue solemnising marriages for the State if next month's referendum results in a change in the definition of marriage.
Spokesman Martin Long said this is also an important matter for the State if three-quarters of its current cohort of solemnisers who are Catholic priests were to withdraw from the civil process.
Mr Long said that the Irish bishops had no plans to discuss the question formally between now and polling day on 22 May.
He was commenting after confirmation at the weekend that the Catholic Church may no longer perform the civil aspects of weddings if the same-sex marriage referendum is passed.
This is because it would mean there were different definitions of marriage between the Church and the State.
In its submission to the Constitutional Convention in 2013, the Irish Catholic bishops warned that the church could no longer perform the civil aspects of weddings if marriage is extended to same-sex couples.
Ahead of the same-sex marriage referendum, a spokesperson for the bishops said nothing had changed, but no formal decision on the issue had been made.
Mr Long told the Irish Times that guidelines for dioceses would be considered by one of the hierarchy's sub-committees, the Council for Marriage and the Family. He said that this would happen later this month.
If the Catholic Church refuses to carry out the civil aspects of weddings, then people who get married in Catholic churches would also have to go elsewhere to have their marriage recognised by the State.
The bishops' submission in 2013 stated that: "It is important to note that in Ireland the church and State co-operate closely in the solemnisation of marriages.
"Over 70% of marriages in the Republic are celebrated by couples choosing the Christian celebration of marriage with both elements (civil marriage and church marriage) taking place within the same ceremony.
"Any change to the (State's) definition of marriage would create great difficulties and in the light of this if there were two totally different definitions of marriage the Church could no longer carry out the civil element."
Mr Long told RTÉ News that this matter is of such importance that only a full conference of the country's bishops can make a decision on it.
Their next meeting is scheduled for the second week in June, more than two weeks after the referendum.
Doubt about whether Catholic clerics will boycott the civil ceremony of marriage and limit themselves to administering the church sacrament will hang over the remaining 37 days of the referendum campaign.
Mr Long emphasised that this was a genuine debate within the Catholic hierarchy and that it was not being used by them as a threat against the 'Yes' campaign.
Atheist Ireland welcomed "the threat by the Irish Catholic Bishops that the church may no longer perform the civil aspects of weddings, if marriage is extended to same-sex couples.
It said: "We believe a formal separation of the religious elements of a church marriage, and the civil elements of a state marriage, would be a good thing for Irish society."
Meanwhile, Dr Richard O'Leary of the Faith in Marriage Equality (FiME) group said "if the Catholic Bishops decide to withdraw the facility they should not seek to lay the blame on same-sex couples because they are allowed to have a civil marriage ceremony at a civil registration office."
He added: "If the Catholic Bishops decide not to facilitate the signing of the civil marriage register at the church premises, these couples would only have to do what is the norm in many European states, including France i.e. sign it on a separate occasion."