The Argentine-born pontiff said the Church, which last month named a high-level group on the scandal including an abuse victim, had to take an stronger stand on a scandal that has haunted it for more than two decades.
"I feel compelled to personally take on all the evil that some priests - quite a few in number, (although) obviously not compared to the number of all priests - to personally ask for forgiveness for the damage they have done for having sexually abused children," he told members of the International Catholic Child Bureau.
"The church is aware of this ... personal, moral damage carried out by men of the church, and we will not take one step backward with regards to how we will deal with this problem, and to the sanctions that must be imposed.
"On the contrary, we have to be even stronger. Because you cannot interfere with children," Francis said in unscripted comments as he addressed the children's rights body.
The comments, originally in Spanish, were translated by the Vatican Radio news service.
Francis did not specify whether "sanctions" would be church-enforced or involve civil justice authorities. In February the United Nations Committee on the Rights of the Child accused the Vatican of systematically turning a blind eye to decades of abuse and attempting to cover up sex crimes.
The scathing report urged the church to immediately hand over its records on the abuse of tens of thousands of children, immediately remove anyone suspected of abuse from their post and refer the matter to civil legal authorities.
Criticism that Francis has not taken a bold enough stand on the issue, and did not meet with sexual abuse victims in Italy and in a July trip to Brazil, has been a rare black spot in the overwhelmingly positive response to the pontiff in the 13 months he has been in office.
The Survivors Network of those Abused by Priests (SNAP), which advocates for child protection and urges greater transparency in the church, on Friday said Francis' words should be received with caution.
"We beg the world's Catholics: be impressed by deeds, not words. Until the pope takes decisive action that protects kids, be skeptical and vigilant," SNAP Outreach Director Barbara Dorris said.
"This may be the first time a pope has talked of sanctions against complicit bishops. But that is all it is: talk."
The church has been accused of condoning the actions of bishops who moved known abusers from parish to parish, allowing abuse to continue.
Under Francis' direction, the Vatican announced in December the creation of a new dedicated group to help the church deal with the abuse crisis. Its members were named in late March.
The group of clerics and lay people includes Marie Collins, a survivor of abuse in Ireland in the 1960s who has campaigned for the protection of children and for justice for victims.
Child abuse litigation has cost the Catholic Church some $3 billion in settlements in the United States alone, and shaken the moral authority of leaders of the world's largest religious denomination.