Cardinal Egan leads more than two million Catholics
In a letter to churchgoers, Cardinal Edward Egan said he regarded sexual abuse of children as an abomination.
The cardinal's message comes only days after Pope John Paul broke his silence on a wave of sex scandals which have battered the church's reputation.
Recently a major paedophile scandal has engulfed the church in the US, and clergy have been involved in cases of sexual abuse and harassment across Europe and in Australia.
Reporting abuse
Cardinal Edward Egan - the spiritual leader of about 2.4 million Catholics in New York - said that priests who abuse children would be removed from their parishes.
In a letter distributed at services for the start of Holy Week, Cardinal Egan told Catholics they should report allegations of abuse by a priest "directly and immediately".
But he stopped short of undertaking to pass on all such accusations to the civil authorities, saying they would be informed "if there was reasonable cause to suspect abuse".
The archbishop defended himself against allegations which surfaced in Connecticut - where he became bishop in 1988 - that he had allowed priests guilty of sexually abusing children to go unpunished.
Press reports have suggested that in several cases where priests were accused of such abuse, they were sent for counselling and moved to new posts, rather than reported to the police or defrocked.
But Cardinal Egan said in his letter that the cases in question occurred before he became bishop.
Criticism at home
His letter came amid indications that many Catholics in the US are unhappy at the way the church has dealt with the issue of child abuse.
A poll of New York Catholics carried out for the New York Daily News suggested that 68% disapproved of the leadership's handling of the crisis.
A separate survey for Newsweek magazine found that three-quarters of US Catholics thought the Church had been too lenient with priests.
The Vatican has frequently been criticised for its slow response to accusations of sexual misconduct, and its tendency to regard such reports as attempts to discredit the Church.