The Association of Catholic Priests in Ireland is to write to the Vatican's Congregation for Bishops expressing its members' "grave disquiet" over the current selection process for Irish bishops.
Augustinian Fr. Gabriel Daly said that the 1968 papal encyclical had never been accepted by the church at large. Daly also condemned the church over its treatment of women.
"Throughout the debate and the discussion, we did ask people to try to be respectful and inoffensive in language," Archbishop Eamon Martin said.
Catholic Ireland has become the first country to introduce gay marriage by popular vote, with 62 percent voting "Yes" in a referendum on Friday.
Archbishop Diarmuid Martin of Dublin said he would seek assurances from religious congregations operating in his diocese that they are rigidly following child protection guidelines after a fresh round of audits raised serious concerns.
In a statement Tuesday, Martin said it was "appalling" that some major religious congregations had delayed fully implementing the church's child protection guidelines and that, in some cases, this process only really got underway in 2013.
Martin said the delays left him "seriously concerned."
"To seek to re-define the nature of marriage would be to undermine it as the fundamental building block of our society," the Irish bishops' conference said.
The Irish government established a working group to address details emerging about Catholic-run, state-funded mother-and-baby homes and the burial of deceased children.
Irish bishops have come in for sharp criticism after deciding they will not publish the results of the Vatican survey on the family.