The pontiff also said bishops and religious superiors who cover up for them will be held accountable.
Francis met for the first time with his sex abuse advisory commission, a group of outside experts named in 2014 to advise him and the Catholic Church on best practices to keep pedophiles out of the priesthood and protect children.
The commission has held educational workshops in dioceses around the world, but has faced such stiff resistance to some of its proposals at the Vatican that its most prominent member, Irish abuse survivor Marie Collins, resigned in frustration in March.
The commission's statutes and membership are up for review, and it remains to be seen if survivors of abuse will be included in the new membership.
Cardinal Sean O'Malley, the archbishop of Boston and head of the commission, told the pope the commission had "benefited greatly" from listening to survivors, but made no mention of whether any were under consideration for membership.
On the membership front, he said only that the commission was seeking "representatives from churches in different parts of the world".
Currently, non-church experts fill the ranks, including noted sociologists and psychologists in the field of abuse and child protection.
In his remarks, Francis renewed his pledge of "zero tolerance" for sex abuse.
He stressed his "profound pain" and shame that children were harmed by priests and those "who should have been the most worthy of trust".
"I repeat today that the church will respond with the application of the firmest measures possible against all those who betrayed their call and abused children of God," Francis said, adding that such sanctions must be applied to all those who work in church institutions.
He recalled that he had approved new rules to sanction bishops who covered up for paedophiles with negligence.
Left unsaid was the fact that Francis scrapped a proposed tribunal to prosecute such bishops canonically, which had been a key proposal by his advisory commission.
The tribunal was ditched after Vatican officials raised a host of legal and procedural problems that had simply never been worked out before the tribunal section was announced to great fanfare by the commission.
