During his visit to Chile in January, Francis upset abuse survivors and their loved ones when he dismissed the allegations against Barros as "calumny", saying there was no evidence and that he had never seen proof against the bishop.
Cruz, whom the pope hosted at his Vatican residence and met individually along with two other victims, said the pontiff was "contrite" and said he had been "part of the problem".
Despite a strong Catholic tradition, Chile is witnessing a growing rift between the people and the Church, sharpened by the string of sexual abuse scandals.
In addition to the 61-year-old Barros, of Osorno, the pope accepted the resignations of Bishop Gonzalo Duarte of Valparaiso and Bishop Cristian Caro of Puerto Montt.
It was the Pope's 2015 decision to name Bishop Barros to lead the small, southern Diocese of Osorno that sparked the abuse controversy in the country.
The pope accepted Barros' resignation despite previous attempts to defend the bishop. The leader of the Roman Catholic Church accepted Barros's resignation as well as those of two others in Chile.
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It was not immediately clear what specific progress, if any, had been made in preliminary discussions between United States and North Korean officials.
"A new day has begun in Chile's Catholic Church!" tweeted Juan Carlos Cruz, the abuse survivor who denounced Barros for years and pressed for the Vatican to take action.
After he returned to the Vatican from that trip, Francis sent the Church's top sex crimes expert to Chile, to investigate further.
Karadima, a charismatic cleric who was a mentor for Barros and other priests, was sentenced by the church in 2011 to a lifetime of penance and prayer for the sex crimes he is accused of.
Those findings, which leaked to the media while the Chilean bishops were at the Vatican, have opened a Pandora's Box of new accusations that recently led Francis to become the first pope to refer to a "culture of abuse and cover-up" in the Catholic Church.
The two investigators will meet Wednesday with Canon law experts from Chilean dioceses who will provide "technical and legal assistance" in order to "provide adequate responses to each case of child sexual abuse committed by clerics or religious", Scicluna told reporters.
"The resignation of these bishops should not dilute their criminal responsibility", he said.
The pope said sorry for unwittingly "wounding" Karadima's victims who say Barros, one of the charismatic Karadima's proteges', shielded the abuser from justice.
The eight-page letter, according to CBC, graphically detailed sexual abuse at the hands of a priest, as well as the subsequent coverup by Chilean church authorities.
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