The church “recognizes the sins of some of her members: the sufferings, the experiences and the pain of minors who were abused sexually by priests. It is a sin that shames us,” he said in a letter made public on Monday.
“I would like us to renew our complete commitment to ensuring that these atrocities will no longer take place in our midst,” he added in the letter, addressed to the world's bishops to mark the Massacre of the Innocents on December 28th.
“Let us find the courage needed to take all necessary measures” to protect children.
“In this area, let us adhere, clearly and faithfully, to 'zero tolerance',” he said.
A string of historic paedophilia cases in North America and Europe has unleashed widespread criticism of the Catholic hierarchy, including allegations that in some cases bishops were aware of sexual predators among the priesthood but failed to curb them.
Francis came to power in 2013 promising a crackdown on cover-ups and a zero tolerance approach to abuse itself, but victims' groups have expressed discontent with his record on ridding the church of the taint of paedophilia.
In June, the pope announced that Catholic bishops guilty of negligence in child abuse cases can now be dismissed from office.
A “college of legal experts” – cardinals and bishops – was set up to help the pope arrive at a definitive decision in each case.
But a US group representing victims of paedophile priests accused the Vatican at the time of seeking to put a brake on efforts to stop abusers and bring them to justice by creating extra red tape.