In a letter to 32 Chilean bishops released by the Vatican, Francis said he intended to summon them to Rome to discuss an investigation into an alleged cover-up by Bishop Juan Barros of abuse by paedophile priest Fernando Karadima during the 1980s and 1990s.
Francis expressed his "shame" and "pain" for the suffering of the victims and pledged to meet them.
"I have made grave mistakes in the assessment and my perception of the situation, especially due to a lack of truthful and balanced information," Francis wrote.
He made no specific mention of Barros, who was appointed Bishop of Osorno in Chile, despite being accused of concealing and even witnessing abuse carried out by Karadima. A 2,300-page report sent to the pope includes testimony gathered from 64 people in New York and Santiago.
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The pope asked the bishops to Rome to discuss the findings of the probe by Archbishop Charles Scicluna and requested their "collaboration and assistance" in finding measures that can "repair the scandal as much as possible and restore justice".
"The present difficulties are also an opportunity to restore confidence in the Church, a confidence broken by our mistakes and sins," Francis wrote.
'Everything is slander'
During a trip to Chile in January, the pontiff had strongly defended Barros, who appeared at public masses celebrated by the Pope in three different Chilean cities, causing a public outcry. Francis said that he was convinced of Barros' innocence and demanded "proof" of abuse before he would speak out against him.
"There is not a single piece of proof against him. Everything is slander. Is this clear?" Francis said.
However, he later apologized to the victims and dispatched Scicluna, a renowned Vatican investigator, to Chile to collect evidence. Scicluna returned at the end of February. Karadima, an influential Chilean priest, was convicted by the Vatican in 2011 of abusing teenage boys and sentenced to a life of penitence. Civil charges against him in the Chilean courts were dismissed because of a lack of evidence.
The president of the Episcopal Conference of Chile, Bishop Santiago Silva, said that the church "had not done enough" in the case.
"Our commitment is that this does not happen again," he added.
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Silva said the meeting of Chilean bishops with the pope in Rome would take place on the third week of May. Scicluna, Archbishop of Malta, was until 2012 a prosecutor in the Vatican Court to investigate cases of paedophilia among priests, making a name for himself with his determination.
He allowed the opening of an investigation into Father Marcial Maciel, Mexican founder of the congregation of the Legionaries of Christ and the perpetrator of numerous cases of paedophilia.
Since taking over in March 2013, Francis has championed the cause of the marginalised and launched a reform agenda. But sex abuse scandals have haunted his papacy and the Vatican announced it was reviving its anti-paedophile panel in February.
The pope has often spoken out about sexual abuse, and has vowed zero tolerance towards what he has described as a "great humiliation" for the Catholic Church.
But many victims remain bitter over alleged coverups and Church inaction over the years.