According to the statement the Cardinal and other Church lawyers understood at the time the interviews took place in 1975 that the oaths would no longer be binding when the taking of evidence from all witnesses was complete.
In the oaths, which the statement quotes, the two teenage victims undertook to talk to no-one about their interviews except to the people who were taking the evidence.
They also pledged that they had told the truth, the whole truth and nothing but the truth.
The statement was issued to correct a version of the oath published yesterday by a newspaper.
The statement reiterated that the intention of the oaths was to avoid potential collusion in the gathering of the enquiry's evidence and to ensure that the process was robust enough to withstand challenge by the perpetrator, Fr Brendan Smyth.
Earlier, Auxiliary Bishop of Down and Connor Donal McKeown defended Catholic Primate of All-Ireland Seán Brady's handling of allegations of abuse by paedophile priest Brendan Smyth.
Last week, it was revealed that in 1975 Cardinal Brady - then a priest - was present when two young victims of the late Fr Smyth were asked to sign an oath of secrecy and had not informed the statutory authorities.
Speaking on RTÉ's Morning Ireland, Dr McKeown said Cardinal Brady made a 'bad decision', which he regretted very much.
He also said that people had a right to be sceptical if the current leadership of the Catholic Church fails to address the crisis over clerical child sex abuse.
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SIC: RTÉ