Pope Francis has written to bishops around the world saying that they must subscribe to a policy of "zero tolerance" for clergy who sexually abuse children and described such abuse as "a sin that shames us".

In a strongly-worded letter sent on 28 December but released by the Vatican yesterday, the Pope said: "I would like us to renew our complete commitment to ensuring that these atrocities will no longer take place in our midst."

Since his election in 2013, Francis has taken some steps to root out sexual abuse in the Church and to put in place practices to protect children. But victims' groups say he has not done enough, particularly to hold to account bishops who tolerated sexual abuse or covered it up.

"[The Church] recognises 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," Francis wrote in the letter.

"I would like us to renew our complete commitment to ensuring that these atrocities will no longer take place in our midst. Let us find the courage needed to take all necessary measures and to protect in every way the lives of our children, so that such crimes may never be repeated. In this area, let us adhere, clearly and faithfully, to 'zero tolerance'."

The comments – included in a letter about the plight of vulnerable children in general – were some of his most comprehensive on abuse.

Francis, who has met victims of sexual abuse several times, both in the Vatican and on some of his foreign trips, said: "We join in the pain of the victims and weep for this sin – the sin of what happened, the sin of failing to help, the sin of covering up and denial, the sin of the abuse of power."

In 2015 Francis ordered the trial and defrocking of a Polish archbishop accused of paying for sex with minors in the Dominican Republic.

The year before he set up a Vatican commission, including some victims, to advise local churches on how to prevent abuse. But some members have complained about the slow pace of change in the Vatican.

Francis also approved the establishment of a Vatican tribunal to judge bishops accused of covering up sexual abuse or failing to prevent it. But the proposal has so far stalled.

Church sexual abuse broke into the open in 2002 when it was discovered that US bishops moved abusers from parish to parish instead of defrocking them. Similar scandals were later discovered around the world and tens of millions of dollars have been paid in compensation.

Additional reporting by Reuters.