Cardinal Sean Brady said he was following bishops' orders
The head of Ireland's Catholic Church "should consider his position", Martin McGuinness has said.
As a priest in 1975 Cardinal Sean Brady was at meetings where children signed vows of silence over complaints against paedophile priest Fr Brendan Smyth.
The Northern Ireland deputy first minister questioned how many other children were asked to stay silent.
However, NI Secretary of State Shaun Woodward said people should not "rush to judgement" on the issue.
Smyth was at the centre of one of the first paedophile priest scandals to rock the Catholic Church in Ireland.
The Northern Ireland-born cleric was eventually convicted of dozens of offences against children over a 40-year period.
But despite allegations being previously investigated by church officials, including the current Irish primate, Sean Brady, as far back as 1975, it was almost 20 years before he was jailed.
Mr McGuinness, who is in Washington for the annual St Patrick's Day celebrations, said the current controversy was a "grave situation".
He added: "I cannot stand back from this. As someone who believes in the Catholic religion, I think many Catholics across the island of Ireland will share my great sense of unease about what we have heard over the past couple of days.
"I am someone who passionately believes in the protection of children. Under no circumstances can we ever see again a circumstance where people have the opportunity to abuse our children."
However, Father Stephen Kearney, a parish priest in Newtownstewart, County Tyrone, said the intervention of the former IRA commander was "clouding the water".
He added: "While I agree with the sentiments Martin McGuinness has expressed, I think shouting it from 5,000 miles away is not particularly helpful.
"I think that he might have to consider his position when, thirty years ago through his actions, much more serious things happened."
Cardinal Brady has said he will only step down if asked to by the Pope.
Archbishop of Dublin Diarmuid Martin said on Tuesday he would not call for his superior to resign.
Ireland's second most senior Catholic said resigning was a personal decision but the most important issue was that the entire truth comes out.
He added: "Brendan Smyth should have been stopped from the very first time it was known that he was abusing."
Irish cabinet minister John Gormley said Cardinal Brady should examine his conscience, describing it as "a case of evil triumphing while a good man stood back from a situation".
The Green Party leader and environment minister said it was "a deeply regrettable situation".
On Tuesday, the Catholic Church in Ireland released more details about why Cardinal Brady asked the two victims, aged 10 and 14, to sign secrecy agreements.
The church said two boys were asked to sign oaths "to avoid potential collusion" in evidence-gathering.
It added this would ensure that the complaints could "withstand challenge."
The church statement does not explain why either Cardinal Brady or his superiors at the time did not share their information with the police.
Critics of the cardinal have accused him of colluding with clerical child sexual abuse and pressuring victims to remain silent.
The Rape Crisis Network Ireland (RCNI) said Cardinal Brady's position had become untenable.
"Cardinal Brady is personally implicated in collusion with clerical child sexual abuse," RCNI director Fiona Neary said.
"In recent public statements regarding clerical child abuse he did not make public his role in pressuring and bullying victims to remain silent. He did not make public his own failures to disclosure a known abuser to civil authorities.
"Sexual abuse that could have been prevented was not, and Brendan Smyth continued to abuse children."