Francis made the off-the-cuff remarks after coming under criticism from victims' advocacy groups for a perceived lack of attention to the problem and ongoing demands that he sanction bishops who covered up for pedophiles.
In his remarks to members of the International Catholic Child Bureau, a French Catholic network of organizations that protects children's rights, Francis said he felt "called to take it upon myself" and "ask forgiveness" for the evil that some priests had committed against children.
"The church is aware of this damage," he was quoted as saying by Vatican Radio. "We don't want to take a step back in dealing with this problem and the sanctions that must be imposed. On the contrary, I think we must be even stronger! You don't play around with the lives of children."
Last month, Francis named the initial members of a commission to advise him on best practices to combat sexual abuse in the church. Half of them are women and one was assaulted by a priest as a child.
The Vatican has said the members will draft the statutes of the commission and would look into the legal "duties and responsibilities" of church personnel, a suggestion that they might take up the critical question of disciplining complicit bishops. Church law provides for sanctions if a bishop is negligent in carrying out his duties, but to date no bishop has been disciplined for protecting an abuser.
Francis named the commission members after coming under fire for taking no action since the commission itself was announced in December. Victims groups also have been irked that he hasn't met with survivors and recently told a newspaper that the church had been unfairly attacked for its abuse record.