His comments were made in the foreword to a new memoir by a survivor of clerical abuse who was first raped by a priest when he was eight years old.
Father, I Forgive You: Abused But Not Broken was written by Swiss man Daniel Pittet, 58. In it, the pontiff called sexual abuse "an absolute monstrosity, a terrible sin that contradicts everything that the Church teaches".
In the foreword, published on Wednesday by the German daily Bild, the pope said the fate of abused children weighed on his soul, especially those who had taken their own lives.
He said: "We will counter those priests who betrayed their calling with the most strenuous measures. This also applies to the bishops and cardinals who protected these priests - as happened repeatedly in the past."
Since his election in 2013, Pope Francis has said he will take a "zero tolerance" approach towards clergy who sexually abuse children.
In a letter released last year by the Vatican, he said: "I would like us to renew our complete commitment to ensuring that these atrocities will no longer take place in our midst."
However, victims have criticised the Vatican for not doing enough to prevent it.
Pope Francis praised Pittet - who endured four years of rapes, abuse and exposure to pornography - for having the courage to tell his stories and forgive his abuser 44 years after he was first molested.
According to excerpts released by German publisher Herder, Pittet indicates that his act of forgiveness had nothing to do with human justice or denial.
He wrote: "Forgiveness does not heal the wounds or wipe away the misery ... forgiving him has allowed me to burst the chains that bound me to him and prevented me from living."
