The Diocese of Dromore has said it is committed to doing what it can to help bring healing to the survivors of clerical sexual abuse within its churches.
The Northern Ireland diocese includes parts of County Antrim, County Down and County Armagh.
Victims of the paedophile priest Malachy Finnegan will be eligible for support. Finnegan was alleged to have committed sex crimes with children in the diocese across four decades, before his death in 2002.
The Diocese of Dromore said in a statement that it: "apologises unreservedly for the hurt and damage caused to victims and survivors of any priest or church representative acting under its authority. The Diocese of Dromore finds such behaviour towards children and vulnerable people abhorrent, inexcusable and indefensible."
The diocese said that Archbishop Eamon Martin, the Catholic Archbishop of Armagh and the Primate of All Ireland, has met with a number of survivors and examined the existing legal claims against the diocese, leading to him wishing to start a resolution "to enable the provision of financial and other supports for survivors without undue further delay."
"This Redress Scheme will be open to victims and survivors of child sexual abuse suffered at the hands of representatives of the Diocese. It endeavours to ensure a process which is victim-centred and aims to provide victims with recognition and reasonable compensation without the need for lengthy investigation and litigation."
The 'redress' could be financial, a personal apology on behalf of the diocese, pastoral support or the provision of counselling by third party Towards Healing - an independent organisation for people who have experienced religious abuse in Ireland.
The Diocese said it "is willing to commit whatever resources it has available for the purpose of redress to this scheme, even if that should exhaust those resources."
The scheme will respond to applications where there are allegations of sexual abuse or grooming, including emotional abuse, which occurred when the applicant was under the age of 18. Applications will be assessed by an independent panel.
The Church said the process will fall outside the civil litigation process and be comparable to a mediation; informal in nature but intended to be binding on the parties, should a resolution be agreed.
Archbishop Eamon Martin has also committed to meeting with those victims who wish to share their story with him and to consider with him other ways in which their pain can be acknowledged and their healing assisted.