The Tánaiste has said the marriage referendum only applies to civil marriage and will not interfere with religious ceremonies.
The Catholic Church has said it would withdraw from registering civil marriages if the referendum on same-sex marriage passes later this month.
Joan Burton said the amendment to the Constitution would not change the meaning of marriage, but rather extend it to gay and lesbian couples.
The Tánaiste said that it was for the Church to decide how they choose manage their own Catholic marriage ceremonies.
Catholic Primate of All Ireland Archbishop Eamon Martin said this weekend that the Church could not support the amendment to the Constitution as it would place the union of two men, or two women, on a par with that between a husband and wife.
The Tánaiste said: "In respect of Archbishop (Eamon) Martin's comments in relation to registration - that's a matter and decision entirely for any Church as to whether or not, after the marriage is completed, they will have a registration process.
"That's entirely a decision for them and I totally respect whatever it is they want to do in that respect."
Yes Equality spokesperson Grainne Healy said: "One issue discussed by the Archbishop in his interview was the possibility of the Catholic Church refusing to perform the civil aspect of marriage in Ireland.
"However, in England, Wales and Scotland, the Catholic Church have continued to perform civil marriage as part of the religious service following the introduction of civil marriage equality there."