The Catholic Primate of All Ireland, Archbishop Eamon Martin, has told Pope Francis that the publication of the report by the Historical Institutional Abuse inquiry serves as a reminder that much remains to be done if the church in Ireland is to continue along the path of penitence, reparation, healing and renewal.

Dr Martin, who is Archbishop of Armagh, said that the publication is a very significant moment.

Speaking on RTÉ's News At One, he said it is yet another moment where "all of us" are confronted by what, he said, has been a dark and disturbing chapter in the life of the church and society.

"We always need to be alert with regards to this issue. What remains to be done is always being on the alert to assure that these despicable things don't happen anymore in the future and that applies to everyone in the church and, indeed, in all of the society."

He said there has been major changes to how life in the church in Ireland has changed over the last number of years and this was discussed at the meeting with Pope Francis in the Vatican this morning.

Meanwhile, the orders investigated by the inquiry have been reacting to the report.

A statement issued on behalf of the Sisters of Nazareth Order said it will consider all the matters raised and the recommendations made in the report.

"We again apologise to anyone who has suffered abuse whether psychological, physical, sexual or neglect on any occasion when the sisters' standard of care fell below what was expected of them.

"It was always the desire of the order to provide a safe place for children and when we failed on any occasion, we want to express our deepest regret.

"This has been a traumatic time for those survivors and victims who have come forward however; we sincerely hope it has also been an opportunity to find some relief.

"This has been an opportunity for many to tell their story, to be heard and to have their experience formally recorded for history. We hope that it has aided or at least started a period of recovery for them."

The Congregation of Our Lady of Charity of the Good Shephard, which ran houses in Derry, Newry and Belfast, says it apologises unreservedly to those former residents whose care fell short of what they needed and deserved.

But it also said it acknowledges the efforts made by its sisters and wants to recognise the work of its sisters today, many who gave their entire lives to childcare.

It added that in circumstances which were often complex and challenging, its work in Northern Ireland has always been informed by the vision of the order's foundress in helping vulnerable children and women in society.

The statement ended by paying tribute to the dedication of Anthony Hart, the panel members, the inquiry staff, and to all those who participated in the inquiry process.

In a statement, the Irish Norbertines says it recognises "the tragic harm and hurt caused to innocent children by Brendan Smyth, a deceased member of our community, as outlined in the report, published today".

It said: "We again unreservedly apologise most sincerely for the hurt and harm caused to so many young people, while also accepting that our management of the man concerned and the accusations presented to us was grossly inadequate."

The De La Salle Brothers, in a statement from Brother Francis Manning, said: "We accept and deeply regret that boys in our care were abused.

"We offer our sincere and unreserved apology to all those whom we failed to protect.

"The De La Salle Order has previously acknowledged that some of its members and lay staff abused innocent victims whilst at Rubane Boys' Home or St Patrick's Training School."

The Sisters of St Louis said they accepted the report: "We are saddened that any child suffered while under our care at the former St Joseph's Training School, Middletown and we offer a heartfelt apology.

"We appreciate how difficult it must have been for the eight former residents to come forward to tell their stories and hope that the conclusions of the inquiry will bring healing and hope to their lives."

The One in Four group has welcomed the publication of the report.

Executive Director Maeve Lewis said: "The Hart Report documents the unspeakable cruelty to which the most vulnerable children in Northern Ireland were subjected over decades while in the care of the state.

"Vicious physical abuse, repeated sexual abuse and neglect were the routine experience of the children.

"Many of them have endured the impact of this inhumane treatment throughout their lives. Judge Hart describes catastrophic failures of the state agencies, religious congregations and the church authorities to properly monitor the care of the children.  

"The shocking revelations in Northern Ireland mirror those exposed by the Ryan Report (2009) into institutional abuse in the Republic."

Services continue to be available for those affected through the HIA Support Service, +4428 90 75 01 31.

The inquiry has also recommended some organisations that are available to those affected by sexual violence and abuse