Several members of the Chilean church hierarchy are accused by victims of ignoring and covering up child abuse by pedophile priest Fernando Karadima during the 1980s and 1990s.
Francis earlier this month promised "changes" to the Chilean church to "restore justice" after reading the conclusions of an investigation into the abuse.
"I must say with shame that we did not listen and react in time" over the allegations, the pope said in the letter, released by Chile's Episcopal Conference at a news conference.
The Argentine pope also announced a new trip soon to Chile by Archbishop Charles Scicluna and Father Jordi Bertomeu, who visited Santiago in February to talk to the victims.
Francis has apologized to the victims, three of whom he met with recently.
On Friday and Sunday, he is to receive seven more victims of Karadima, who was suspended for life by the Vatican.
On May 18, 34 Chilean bishops announced their resignation over the scandal, after Francis summoned them.
Since 2000, about 80 Roman Catholic priests have been reported to authorities in Chile for alleged sexual abuse.
Some analysts note that Chile's long tradition of having the church not subject to civilian law lent itself to impunity and cover-ups.
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