The Taoiseach has said that the Government accepts the 20 recommendations contained in the report into child abuse and is committed to their full implementation.
Mr Cowen acknowledged the statement from the Christian Brothers who said they would be reviewing how best to use their resources to the benefit of victims and called on the remaining religious orders to make a substantial additional contribution to the victims of abuse.
Green Party leader John Gormley saluted the brave people who - sometimes at great risk of prolonging their own hurt - campaigned long and against adversity for recognition that these great wrongs occurred and sought provision of some semblance of redress.
Mr Gormley said ‘I was saddened by the tardy and grudging nature of religious orders' responses over the last week.’
Mr Cowen earlier told TDs the controversial indemnity deal concluded in 2002 could not be reopened but there was nothing to prevent religious orders making additional voluntary contributions to the fund compensating victims of abuse if they wanted to.
Former Education Minister Michael Woods, who negotiated the agreement, interrupted Leaders' Questions to protest about remarks from the Labour party which he described as scurrilous.
Eamon Gilmore had claimed that he had excluded the Attorney General from the negotiations, a charge Dr Woods hotly denied.
The Taoiseach earlier said he intended to invite the congregations named in the Ryan report to a meeting to discuss what further steps they intend to take to address victims' needs.
Brian Cowen said that although legal advice has suggested that the compensation deal negotiations cannot be reopened, this does not hinder the religious from making voluntary financial contributions.
He said there was moral responsibility on the religious orders to make a further contribution to show that every possible effort is being made to address the wrongdoing.
Mr Cowen earlier welcomed the statement from the Christian Brothers offering further reparation for the abuses by members of their congregation uncovered in the Ryan report.
They have offered to consult with former residents of their industrial schools, with the Government and others to review how their resources can best be applied in reparation for abuses.
The Brothers say they accept, with shame, the findings of the Child Abuse Commission and that their congregation is deeply sorry for the hurt its members have caused not just in the past, but through the inadequacy of responses over recent years.
A sombre Dáil saw Fine Gael leader Enda Kenny offering the hand of unity to Brian Cowen, urging that the House agree a motion that reflects the widespread outrage at the contents of the report.
Brian Cowen also reiterated the earlier apology to those abused from his predecessor and praised this afternoon’s statement from the Christian Brothers offering further reparations.
He said he hoped the other orders would issue similar responses.
CORI: Orders to provide more resources
The Conference of the Religious in Ireland has said the refusal by religious orders to renegotiate the compensation deal agreed with the State is not a blocking mechanism or a way of saying no to the survivors.
CORI represents the 18 congregations responsible for institutional abuse of children, among others.
On RTÉ's Morning Ireland, CORI Director General Marianne O'Connor said the orders involved would put more resources, including money, into meeting the needs of abuse survivors directly.
She said that the orders were already supporting former residents and that they were seeking the best way to help those still suffering from the abuse they experienced at the hands of those who ran the institutions.
However, Ms O'Connor said the 2002 deal would not be revisited.
The Cabinet will be briefed by the Attorney General about the legal situation of the deal when it meets later today.
Speaking on RTÉ's Questions and Answers last night, Minister for Transport Noel Dempsey said the religious orders should put money into a trust to help victims, rather than contribute to the State compensation fund.
The report was published last week, a decade after the Commission to Inquire into Child Abuse was set up by the Government.
Following the report there were mounting calls for the religious orders to revisit the deal, which capped their contributions.
Fine Gael Leader Enda Kenny has said religious orders have a moral responsibility to contribute more to help the survivors of institutional abuse.
He said the recommendations of the Ryan report must be implemented in full.
Speaking in Dublin, Mr Kenny said there needs to be a focus on young people now and how they are protected and dealt with.
He said in 2009 the state remains unable to look after children who need care.
Responding to criticism of himself on last night's Questions and Answers programme when a victim accused him of playing politics with the issue, he said if that were the case he would apologise, but he said the matter is way beyond politics or playing politics with it.
Labour Party justice spokesman Pat Rabbitte has called on Taoiseach Brian Cowen to invite CORI to a meeting to discuss reopening the agreement.
Mr Rabbitte described CORI's refusal to do so as a calculated snub to public opinion.