The Catholic Church is "crying" and seeks forgiveness for the pain felt by children abused by priests but also "the shameful sin" committed against them, Pope Francis told bishops in a letter made public on Monday.

"The Church is crying not just at the pain caused by its smallest sons and daughters but also because it knows the sin committed by some of its members," Francis said in the letter to mark Innocents' Day, celebrated on December 28.

"The history of suffering and pain experienced by minors who were sexually abused by priests. This is shameful sin," he added.

The Church "profoundly deplores and asks forgiveness" for individuals who "destroyed the dignity" of children in their charge, he said.

"We share the victims' pain and weep for the sins committed. The sin of failing to help, of covering up and denying and the sin of abuse of power."

The letter also expressed the Catholic Church's contrition for the child sex abuse perpetrated by its members.

"The Church too weeps bitterly over the sins committed by its sons and asks forgiveness," Francis said.

"I want us to renew our full commitment to preventing these atrocities happening again in our midst," the pontiff told bishops, vowing "zero tolerance" towards such crimes in future.

Francis has called for "severe punishment" of paedophiles. He revealed a new church law in 2016 that would punish bishops if they failed to fire paedophile priests.

Bishops have long been accused of moving church members who molest children to other parishes, rather than reporting them to police.

However, doubts remain about the Vatican's commitment to tackling the scandal of paedophile priests, which has severely tarnished the Catholic Church's reputation and cost it $3 billion in settlements in the US alone.