Pope Francis has asked for forgiveness for the "evil" damage to children caused by sexual abusers in the clergy.
He said the abuse was a "moral damage carried out by men of the Church", and that "sanctions" would be imposed.
The statement, made in a meeting with a child rights group, is being described as his strongest the issue so far.
Last month, Pope Francis strongly defended the Roman Catholic Church's record on tackling sexual abuse by priests, following UN criticism.
The Pope set up a committee last year to organise help for victims of clerical sexual abuse but has been accused by some Catholics of dragging his feet in acknowledging the extent of the moral and mental damage caused by paedophile priests, the BBC's David Willey reports from Rome.
The Pope said he had felt compelled to "personally ask for forgiveness for the damage [some priests] have done for having sexually abused children", the Vatican Radio website reports.
He said that the number of priests who had committed abuses were "quite a few in number", although "obviously not compared to the number of all the priests".
"We will not take one step backward with regards to how we will deal with this problem, and the sanctions that must be imposed," he said, adding: "We have to be even stronger".
Alessandra Aula of International Catholic Child Bureau, the children's non-governmental organisation that was at the Vatican for the Pope's address, welcomed his comments.
"The Pope took an unequivocal position on sexual abuse and I think it is a message we all were waiting for," she told BBC World TV.
In an interview last month, Pope Francis defended the Catholic Church, saying: "No-one else has done more [to tackle child sexual abuse]. Yet the Church is the only one to have been attacked."
It came after a UN report accused the Vatican of systematically placing the "preservation of the reputation of the Church and the alleged offender over the protection of child victims" - something the Church has strenuously denied.
The Catholic Church has faced numerous allegations of child sex abuse by priests around the world and criticism over inadequate responses by bishops.
Earlier this year Pope Francis strengthened Vatican laws on child abuse, broadening the definition of crimes against minors to include sexual abuse of children.
While in office, predecessor Pope Benedict XVI apologised to victims of child sex abuse, saying he was "truly sorry" for the "sinful and criminal actions" committed by priests.