The Catholic Communications office has said that the then Fr Brady had no decision-making powers regarding the 1975 inquiry into Brendan Smyth.
In a statement it said that was the responsibility of his bishop and that he was asked to conduct the inquiry because he held a doctorate in Canon Law.
Archbishop of Dublin Diarmuid Martin has said it is very important that the truth comes out about clerical sexual abuse.
He said people wanted the truth but he did not believe extending the Murphy Commission to each diocese would be the best way to use money for child protection.
Archbishop Martin added, however, that it may be the only way necessary to ensure the truth comes out. He said 'there would no healing until we fully address the past'.
He also said that Brendan Smyth should have been stopped from abusing children from the start.
Asked about whether Cardinal Brady should consider his position, Archbishop Martin it was not his job to tell people to resign or to stay on.
Speaking before a St Patrick's Day Ecumenical service in Dublin tonight, he said people should be accountable for what they have done.
Resigning, however, was a personal decision, he said.
Asked about whether he was aware of the revelations about Cardinal Brady before they emerged at the weekend, Archbishop Martin said he was not.
Regarding the two children taking an oath of secrecy, Archbishop Martin said he 'did not know what age they were at the time and the legality'. He said the question of secrecy is very complicated as in continental law, which cannon law is, there is a 'secrecy in all investigations'.
When asked whether Cardinal Brady should have gone to the gardaí, Archbishop Martin said he 'did not have the details and that's up to him to explain'.
Archbishop Martin said he has since spoken to Cardinal Brady by telephone. He also denied that he had been silenced or ostracised by other clergy. He said it was important that he maintains his own independence of thought.
Speaking in Washington this evening, Taoiseach Brian Cowen said: 'Child protection is a very important issue - the societal lessons that have to be learned in Ireland and elsewhere are very keenly felt by the people of Ireland, they want to see it dealt with appropriately.'
He said the question of 'equality before the law is a fundamental principle and we have to make sure that in whatever way issues arise, that they're dealt with regardless of what the circumstance may be.'
Pushed on the issue of whether Cardinal Brady should consider his position, Mr Cowen said 'the leadership I'm giving is that clearly it is important that the State maintains its base and the Church maintains its base - it's not a question for the State to get involved in Church matters nor the Church to get involved in State matters.'
He added: 'I want to make it clearly the case, that this is an important issue and that there are arrangements in place for child protection now that have to be maintained, promoted and defended.'
He said it would be for others to assess if legal issues arise.
Vatican official speaks on responsibility
This afternoon, a Vatican official said that a Roman Catholic confessor can do no more than absolve a sinner, even one who confesses to paedophilia.
The confessor is not required to 'ask the sinner to turn himself in to the authorities,' Gianfranco Girotti said in an interview with the Vatican newspaper L'Osservatore Romano.
Bishop Girotti is responsible for one of the Vatican's three courts. He said: 'The only possible outcome of confession is absolution.'
Asked about recent paedophilia scandals, he said: 'It is not up to the confessor to make (confessions of paedophilia) public, nor to ask the repenter to turn himself in to his superiors.'
Bishop Girotti argued: 'For one thing, the seal of the (confession) sacrament is inviolable, and for another we must not engender mistrust among penitents.’
When a sinner approaches the confessional he ‘must expect only absolution from the confessor, and surely not a judgement or an injunction to confess his crime in public.’
Paedophile priest scandals have rocked several churches around the world as well as in Ireland.
The Catholic Communications Office said that in 1975 Bishop Francis McKiernan advised that the Norbertine order should have Fr Smyth treated by a psychiatrist.
In a statement on the role Cardinal Brady played when he was a priest in dealing with Fr Smyth, a spokesman said the advice was given at the same time that Bishop McKiernan withdrew Fr Smyth's right to celebrate mass, hear confession and perform his other functions as a priest.
The spokesman said the two boys at the centre of the inquiry were asked to confirm the truthfulness of their statements and that they would preserve the confidentiality of the interview process.
He says it was important to ensure the process was robust enough to withstand a challenge by the perpetrator, Fr Smyth.
A spokesman for the Norbertine Order has said that they will not be commenting on the statement.
Victims' groups questions Brady's decision
Meanwhile, another group representing victims of clerical child abuse has questioned Cardinal Brady's decision to remain in office .
Voice of the Faithful, a lay organisation of Catholics, questioned how the Cardinal believed he could now provide the leadership that was needed to draw a line under all that had happened.
The group says it cannot understand why Cardinal Brady believes he should not resign after his own statement in December in which he said he would do so if he thought any failure of his to act had caused a child to suffer.
It says the Cardinal’s failure to challenge the culture of Church silence surrounding clerical child sexual abuse in the period of 1975 to 1994 is a most serious matter and leaves the Irish Catholic Church without a leader that survivors in particular can have full confidence in.
Cardinal Brady has already rejected claims that he failed to act in 1975 when two young victims of the late Fr Smyth were asked to sign an oath of secrecy.
Cardinal Brady said he was not the designated person responsible for contacting the relevant statutory authorities.
On RTÉ's The Frontline programme last night, lecturer at University College Dublin Fr Brendan Purcell said Cardinal Brady had been through a process of learning how to deal with clerical sex abuse and his departure as head of the Catholic Church in Ireland would deprive it of a very experienced leader.
One helpline recorded a significant increase in calls following the latest revelations.
The Rape Crisis Centre said it had to bring in extra staff to cope with the rise in calls last night.
The Dublin Rape Crisis Centre: 1800-778888 (24 hour helpline)
HSE helpline: 1800-235234 (office hours)
One in Four: 01-6624070 (office hours)
The Samaritans: 1850-609090