The head of the Catholic church in Ireland, Cardinal Sean Brady, yesterday rejected growing pressure to resign over his involvement in the country's latest clerical child abuse scandal, insisting that he would stand down only on the Pope's orders.

The position of Cardinal Brady is in doubt following revelations that he was party to the imposition of an oath of silence on two young people complaining of abuse by one of Ireland's most notorious paedophile priests. After two meetings in 1975 the priest, Father Brendan Smyth, went on to abuse many other young people over the following two decades before being jailed.

Yesterday Cardinal Brady apologised to the victims of abuse, saying that with hindsight he should have done more. But when reminded of demands for his resignation, he said: "I've heard those calls. I've said I don't think it was a resigning matter. I've also heard other calls, many other calls, to stay and continue the work of addressing this most difficult problem." And, speaking to the BBC, he insisted that he would "only resign if asked by the Holy Father".

Cardinal Brady's part in gathering evidence against Smyth emerged after he was named as a defendant in a lawsuit filed by one of Smyth's victims. The latest disclosures follow a stream of official reports which have exposed a network of clerical misbehaviour, followed by high-level cover-ups within the church, which have brought much public wrath on the clergy.

Several bishops have resigned, mostly reluctantly and with bad grace, as senior church figures promised that no stone would be left unturned in dealing with the abuse issue.

The irony is that Cardinal Brady was among those vowing that a new era of openness and transparency would replace the traditional secrecy. This new development is seen as the emergence of a skeleton from his own cupboard.

As head of the Irish church he has been generally low-key and self-effacing, and in fact his declared determination to clean up the clerical abuse mess has been a rare example of energy on his part. Since the story broke about his own involvement, however, his tone has switched from the crusading to the defensive.

He said in a statement that when he was a priest he attended two meetings as a part-time secretary to a bishop, acting as a recording secretary.

He added: "At those meetings the complainants signed undertakings, on oath, to respect the confidentiality of the information-gathering process." He said he had passed these on urgently to the bishop, and in doing so had fulfilled his duties.

The Cardinal said he believed the victims' stories. He added in interviews: "Yes, I knew that these were crimes, but I did not feel that it was my responsibility to denounce the actions of Brendan Smyth to the police.

"Now I know with hindsight that I should have done more, but I thought at the time I was doing what I was required to do. There was a culture of silence about this, a culture of secrecy; that's the way society dealt with it."

It has been pointed out that last December he declared: "If I found myself in a situation where I was aware that my failure to act had allowed or meant that other children were abused, well then, I think I would resign."

The Cardinal did not mention that he has been discreetly fending off the civil court case centring on his involvement in the Fr Smyth affair for many years.

Calls for his resignation were led by a number of victims of clerical abuse. One of these, Andrew Madden, said the abuse of children was widespread, adding: "I believe every diocese in the country will have allegations which were mishandled. It's only a case of when people are found out."

An American woman who was decades ago abused by Fr Smyth yesterday accused Cardinal Brady of "having blood on his hands". Helen McGonagle, who is a lawyer handling abuse cases, said of the Cardinal: "He's coming to this issue with unclean hands. Swearing victims to an oath of secrecy ... while others can be harmed – that cannot be tolerated."