However, the Archbishop of Dublin rejected newspaper reports that his comments of last week were "a criticism of Pope Benedict".
In a statement, Archbishop Martin said his comments last week to the Knights of Columbanus were a reaffirmation of the Pope's urgent appeal in his letter to Irish Catholics "to address the problem of abuse that has occurred within the Irish Catholic community and to do so with courage and determination".
He also stood by his statement that "there are still worrying signs that despite solid (child protection) regulations and norms, these are not being followed with the rigour required."
His latest statement rejected as untrue a newspaper's claim that he had backed off his claims of eight days ago that reforms to improve the Church's child protection practices in Ireland were being resisted by powerful forces inside the organisation.
The archbishop said he fully supported the work of the National Board for Safeguarding Children in the Catholic Church and welcomed the publication of its annual report on Monday.
In particular, he noted the view of the board's chairman, John Morgan, that: "Clearly, a cultural correction is required in the Irish Church to deal with the problem of abuse."
The archbishop insisted that norms on their own were not enough to ensure the protection of children, urging that they "required wholehearted and robust endorsement".
He said: "Anything less than a totally robust response will not be enough. There is no room for slippage."
He also highlighted a comment by Ian Elliot ,the head of the Church-funded independent child protection watchdog.
While recognising the significant progress made, Mr Elliot noted: "This has proved to be demanding for some within the Church who have had difficulty in changing their attitudes to fully embrace a single safeguarding approach."
Dr Martin dismissed as "a gratuitous misinterpretation made without any grounds" a newspaper's report that his comments were "a criticism of Pope Benedict".
Meanwhile, victims of clerical abuse have criticised Cardinal Sean Brady's statement of intent to stay on as leader of the Irish Catholic Church in spite of their repeated calls for his resignation over the role he played in the 1975 cover-up of the activities of paedophile priest Brendan Smyth.
Maeve Lewis, executive director of the One in Four victim support group, said: "Cardinal Brady states that he has consulted with survivors. He certainly has not listened to what they have said.
"Survivors who are in contact with One in Four are very clear that they need senior Catholic churchmen to be accountable for what they have done -- and to resign."
SIC: EHie