The orders, 18 in total, have refused to increase their €128 million contribution to a compensation fund for victims of the abuse that is graphically detailed in the exhaustive report.
But they might have to do just that if ordered to by Pope Benedict.
Meanwhile, as authorities look at the prospect of possibly filing criminal charges, the leader of the Catholic Church in Ireland has said that anyone responsible for abusing children in Catholic-run institutions must be held to account.
Cardinal Sean Brady's unprecedented calls came followed the publication last week of the Commission to Inquire into Child Abuse report which probed widespread and systematic abuse of children in state-owned institutions administered by religious orders.
The commission, chaired by Mr. Justice Sean Ryan, concluded that thousands of children suffered physical and sexual abuse over several decades in residential institutions run by religious congregations.
The commission heard from more than 500 witnesses who said they had been sexually abused and there were also many reports of injuries including broken bones, lacerations and bruising.
The report, which makes for shocking reading, describes how children lived in "a climate of fear" in the institutions and finds that "sexual abuse was endemic in boys' institutions."
Cases of sexual abuse were hidden by the congregations that ran the institutions and offenders were transferred to other locations where they were free to abuse again, the report said.
Eight chapters in the report are devoted to the Christian Brothers, the largest provider of residential care for boys in Ireland.
More allegations were made against the Christian Brothers than all other male orders combined.
The report also sharply criticized the Irish government's department of education for failing to carry out proper inspections.
"The deferential and submissive attitude of the Department of Education towards the congregations compromised its ability to carry out its statutory duty of inspection," the report stated.
The inquiry commission, which was set up in 1999, investigated industrial schools, reformatories, orphanages, institutions for children with disabilities and ordinary day schools.
It heard evidence covering the period from 1914 to the present, but the bulk of its work addressed the period from the early 1930s to the early 1970s.
More than 1,700 men and women gave evidence of the abuse they suffered as children in institutions, with over half reporting sexual abuse.
Accounts of abuse given in relation to 216 institutions are detailed in the report, which runs to nearly 3,000 pages.
More than 800 priests, brothers, nuns and lay people were implicated. The final cost of the commission may be over €100 million.
Responding to the report, the Catholic primate, Cardinal Seán Brady, said he was "profoundly sorry and deeply ashamed that children suffered in such awful ways."
He stated: "Children deserved better and especially from those caring for them in the name of Jesus Christ."
The minister for education, Batt O'Keeffe said "the wrongs of the past" could not be undone.
"However, as a responsible and caring society, we must fully face up to the fact that wrong was done and we must learn from the mistakes of the past," he said.
Speaking in the Dáil, Taoiseach Brian Cowen said the government would "carefully study the findings and recommendations."
The Christian Brothers, who are severely criticized in the report, also issued an apology.
"We are deeply sorry for the hurt caused. We are ashamed and saddened that many who complained of abuse were not listened to," a statement said.
"We appreciate that no healing is possible without an acknowledgement of our responsibility as a congregation for what has happened."
The Catholic archbishop of Dublin, Diarmuid Martin, said the stories of abuse were "stomach-churning."
Despite this, the findings will not be used for criminal prosecutions, in part because the Christian Brothers successfully sued the commission in 2004 to keep the identities of all of its members, dead or alive, unnamed in the report.
The order issued an apology Tuesday saying it "accepted with shame" the findings of the commission.
No real names, whether of victims or perpetrators, appear in the final document.
The report has sparked a mixed reaction from victims groups.
The "One in Four" organization, which offers support to victims of abuse, said publication of the report marked a "shameful day" for Ireland.
Child welfare organizations called for a constitutional amendment to protect the rights of the child.
Fergus Finlay, chief executive of the charity Barnardos said: "we must guarantee that the voices of children are never silenced again."
The report recommends an overhaul of the inspection system for childcare services to include unannounced inspections and objective national standards. It also proposes the erection of a memorial to victims of abuse in the institutions.
The Commission to Inquire into Child Abuse is separate from the Residential Institutions Redress Board, which has received some 15,000 applications for financial compensation.
It is expected the total cost of awards by the board will exceed €1 billion, of which €128 million has been contributed by 18 religious congregations.
In the days following the publication of the report, counseling services throughout Ireland reported a significant rise in calls from people seeking help.
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