Pope Francis on Thursday accepted the resignation of two more Chilean bishops caught up in the country's sexual abuse scandal, the Vatican said, bringing to five the number he has accepted so far.

Bishops Alejandro Goic Karmelic of the city of Rancagua and Horacio del Carmen Valenzuela Abarca of the city of Talca would be replaced by commissioners, known as apostolic administrators, a statement said.

Francis accepted the resignations of three other bishops on June 11 after receiving a report by his investigator, Maltese Archbishop Charles Scicluna. 

Last month all of Chile's 34 bishops offered to resign en masse after a meeting with the pope over allegations of a cover-up of sexual abuse.

Goic, 78, issued a statement last month apologising for not acting swiftly when allegations of sexual abuse by priests in his diocese were first brought to his attention.

Valenzuela, 64, was one of four bishops who was trained for the priesthood decades ago by Father Fernando Karadima, Chile's most notorious abuser. Karadima was found guilty in a Vatican investigation in 2011 of abusing boys in Santiago in the 1970s and 1980s. Now 87 and living in a nursing home in Chile, he has always denied any wrongdoing.

Francis told Reuters in an exclusive interview at his residence on June 17 that he was considering accepting the resignations of more Chilean bishops.