The pope’s belief in the bishop’s innocence over the victims’ accusations outraged advocates for abuse survivors, and gave ammunition to those who said the usually politically deft pope had a tin ear when it came to sex abuse. All that pressure prompted Francis to send Archbishop Scicluna to Chile in January “as a result of some information received regarding the case,” the Vatican said at the time.

The pope’s letter released Wednesday had an entirely different tone. He wrote that the investigators sometimes felt “overwhelmed” by “so many victims of grave abuses of conscience and of power and in particular of the sexual abuses committed by various clergymen of your country against minors, who were robbed of their innocence.”

In Chile, the church hierarchy followed his lead. Msgr. Santiago Silva said church leaders “share the pain of Pope Francis,” and added, “we haven’t done enough. Our commitment is that this will never happen again.”

One of the victims, Juan Carlos Cruz, said of the pope’s letter, “It seems like he is ready to make some much-needed changes that will not only affect the church in Chile, which is in dire need of new bishops, and stop the cover-up of sexual abuse, but it would also send a sign to all the world that zero tolerance is zero tolerance.”

The Vatican has repeatedly argued that it is serious about cleaning up what Pope Benedict XVI once called “filth” in the church. On Saturday, the Vatican police arrested Msgr. Carlo Alberto Capella, a former diplomat at its embassy in Washington, where he was suspected of possessing child pornography. The Vatican had recalled him in September amid an investigation by American law enforcement officials, who had sought to strip him of his immunity.

On Wednesday, the pope seemed to seek a silver lining in what has become a black cloud over his pontificate and the Chilean church. “I assure you of my prayers and I want to share with you the conviction that the present difficulties are also an occasion to re-establish the trust in the church, broken by our mistakes and sins, and to heal wounds that haven’t stopped bleeding in Chilean society,” he wrote.

Austen Ivereigh, the author of a papal biography, “The Great Reformer: Francis and the Making of a Radical Pope,” also seemed intent on finding some good in the painful chapter.

“He’s shown he’s determined to defend the innocence of a bishop if there isn’t convincing evidence,” he said of Francis. “But when there is, he’s willing to say sorry and act.”