Deputy First Minister Martin McGuinness has said Cardinal Brady should "consider his position", following revelations that he didn't report complaints about serial abuser Father Brendan Smyth to the authorities in 1975.
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Speaking in Washington ahead of the St Patrick's Day celebrations, Mr McGuinness said he was "dismayed" by the latest revelations to rock the Catholic Church.
"If two children were asked to sign vows of silence, then how many more were asked to do the same thing down the years?" He asked on Tuesday.
"My only conclusion to all of this is that Cardinal Brady has to consider his position".
The head of the church in Ireland has defended his role in the meeting where two children abused by Smyth were asked to take a vow of silence as part of an internal investigation by clergy.
Cardinal Brady, who is being sued by one of the Smyth's victims in Dublin's High Court, has maintained there was no cover-up when he carried out his investigations 35 years ago.
A statement issued by the Church on Tuesday insisted the current cardinal was a junior figure at the time.
In late March 1975, Father Sean Brady was asked by his bishop, Bishop Francis McKiernan, to conduct a canonical inquiry into the allegation of child sexual abuse, the church said.
Father Brady was then a full-time teacher at St Patrick's College, Cavan.
He took notes during the two meetings with children aged 14 and 15 who he believed had been abused by Smyth.
"A week later Father Brady passed his findings to Bishop McKiernan for his immediate action," said the Catholic Communications Office.
The One In Four victims' group executive director Maeve Lewis said: "No-one is disputing that Cardinal Brady was not the most senior person in the investigation into Brendan Smyth.
"But on the other hand, he was a man in his 30s, he must have known what happened was wrong and was a crime."
Cardinal Brady has said he will only step down if told to by the Pope.
On Tuesday, Archbishop of Dublin Diarmuid Martin - the second most senior Catholic in Ireland - said resigning was a personal decision.
The most important issue was that the entire truth comes out, he added.
"Somebody should have stopped him," he said of serial abuser Father Smyth.
"Brendan Smyth should have been stopped from the very first time it was known that he was abusing."
Smyth was at the centre of one of the first paedophile priest scandals to rock the Catholic Church in Ireland.
A seven-month delay in extraditing him to Northern Ireland also led to the collapse of the Irish Government in November 1994.
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