In a statement, Bishop Michael Duignan said his priority is that anyone "betrayed or harmed by Bishop Casey is heard and that their experiences are appropriately acknowledged and recognised".
Bishop Duignan said the diocese adheres to all current procedures for responding to allegations concerning the safeguarding of children as governed by the National Board for Safeguarding Children in the Catholic Church in Ireland.
All safeguarding allegations are reported to An Garda Síochána and the child and family agency Tusla for investigation, he added.
Bishop Duignan said that diocesan safeguarding personnel, along with the bishop, are available to provide pastoral care and support while counselling is also available through the independent professional support organisation Towards Healing.
The statement comes after the former chief safeguarding officer for the Catholic Church in Ireland described Bishop Casey as "a sexual predator".
Ian Elliott makes the comment in an RTÉ documentary, in association with the Irish Mail on Sunday newspaper, broadcast last night.
The programme examined the church's handling of allegations against Bishop Casey, who died in 2017.
It included an interview with one of his accusers, his niece Patricia Donovan, who claimed that he first raped her at the age of five and the sexual abuse continued for years.
Mr Elliot, who has direct knowledge of Ms Donovan's complaint against Bishop Casey, said that he found her account of what she experienced "entirely credible".
In 2019, the Diocese of Galway informed the Irish Mail on Sunday that it had received just one allegation of child sexual abuse against Casey.
It later confirmed that it had a record at that time of "five people who had complained of childhood sexual abuse against Bishop Casey".
These independent accusations relate to alleged events in every Irish diocese where he worked.
The documentary, Bishop Casey's Buried Secrets, also revealed how the Diocese of Limerick paid over €100,000 in settlement to one of his accusers after the bishop's death.
Despite his resignation as Bishop of Galway in 1992, Casey remained a bishop until he died in 2017 and claimed his removal from ministry was unjust.