"I am ashamed, frankly, of my church's failure to be a champion of gay rights and women's rights," former Irish President Mary McAleese has said.
An Irish bishop urged his colleagues to establish a commission to discuss the possibility of ordaining married men.
Bishop Leo O'Reilly of Kilmore also wants the Irish bishops' conference to empower the commission to further study female deacons.
The proposal stemmed from a 10-month listening process that O'Reilly led in the Kilmore diocese, which led to a diocesan assembly and a new diocesan pastoral plan to tackle challenges facing the Catholic church, including the declining number of priests.
"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.
In an open letter, 32 signatories tell Pope Francis that the future of parish life is "massively threatened."
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.
Archbishop Diarmuid Martin of Dublin decried comments from clerics and others who said Pope Francis caused confusion in his calls for an open discussion on how the church should reach out to those who are marginalized, hurt and wounded in their lives during the recent Synod of Bishops on the family.
Martin said he was "quite surprised at the remarks of some commentators within church circles about the recent Synod of Bishops, often making accusations of confusion where such confusion did not exist and so actually fomenting confusion."
The 2013 conclave that elected Pope Francis was "the highlight of my life," said Cardinal Sean Brady, the day the pope accepted his resignation as archbishop of Armagh, Northern Ireland.
Pope Francis "challenges and inspires me" with the "message of God having mercy and at the same time choosing us, despite our sinfulness," the cardinal told people gathered in St. Patrick's Cathedral in Armagh. "It reminds me that I, too, need to say sorry and to ask forgiveness. And I do so again, now."
One of the Irish survivors of clerical sexual abuse who met Pope Francis on Monday described the encounter as a "huge vindication" for her.
The victim, Marie Kane, also asked the pope to remove Cardinal Sean Brady as archbishop of Armagh, Northern Ireland.