'Paedophilia not a criminal condition' - Catholic Archbishop of Durban
The South African cardinal told the BBC that people who were themselves abused as children and then abused others needed to be examined by doctors.
He was one of 115 cardinals who took part in the conclave at the Vatican to elect Pope Francis earlier this week.
The Church has recently been dogged by scandals over clerical sex abuse.
In an interview with the Stephen Nolan programme on BBC Radio 5 live, Cardinal Napier referred to paedophilia as "a psychological condition, a disorder".
"What do you do with disorders? You've got to try and put them right.
"If I - as a normal being - choose to break the law, knowing that I'm breaking the law, then I think I need to be punished."
He said he knew at least two priests, who became paedophiles after themselves being abused as children.
"Now don't tell me that those people are criminally responsible like somebody who chooses to do something like that. I don't think you can really take the position and say that person deserves to be punished. He was himself damaged."
Cardinal Wilfrid Napier's comments triggered immediate criticism.
Barbara Dorries, who as a child was abused by a priest, works for the Survivors Network of those Abused by Priests, which is based in Chicago. She told the BBC: "If it is a disease that's fine, but it's also a crime and crimes are punished, criminals are held accountable for what they did and what they do.
"The bishops and the cardinals have gone to great lengths to cover these crimes to enable the predators to move on, to not be arrested, to keep the secrets within the church."
Michael Walsh, who has written a biography of late Pope John Paul II, said Cardinal Napier's remarks were similar to the position once taken by the Catholic Church in the UK and the US.
"They did actually at one time believe it was a condition that could be dealt with. Many bishops were simply moving priests and trying to disguise the fact that they'd been committing these crimes," Mr Walsh told the BBC.
Marie Collins, who is a victim of abuse, told the BBC: "I think it is appalling that we have a cardinal, a man at this level in the church that can still hold these views. He is totally ignoring the child."
Voice of Russia, BBC