In a letter released by the Vatican, the former pontiff asked forgiveness for any "grievous fault" but denied personal wrongdoing.
A German report into the Catholic Church alleged that he failed to act over four child sex abuse cases.
Then known as Josef Ratzinger, he was archbishop of Munich from 1977 to 1982.
The report by a German law firm alleges that abuse continued under his tenure, and that the priests accused of carrying out the abuse remained active in church roles.
Before the report was released in January, Pope Benedict had denied he had attended a meeting in 1980 about sexual abuse cases when he was archbishop of Munich.
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