The former pontiff spoke of his "profound consternation" that "evil" had entered so deeply into the Roman Catholic faith.
But he denied that he had, either as Pope or previously as head of the Vatican office dealing with abuse cases, tried to cover up the scandals that tarnished the church's reputation around the world.
"That the power of evil penetrated so far into the interior world of the faith is a suffering that we must bear, but at the same time must do everything to prevent it from repeating," he said.
The letter, sent to Piergiorgio Odifreddi, an atheist mathematician, and reprinted by the leading Italian newspaper 'La Repubblica', was the first published statement from Benedict since he said on retirement that he would live out his years "hidden from the world".
The letter, which also discussed topics such as the nature of Catholic belief, the conflict between good and evil, and evolution, came two weeks after 'La Repubblica' published a similar letter from his successor Pope Francis on atheism and agnosticism.
The Vatican said the timing of the two documents was a coincidence.
But the fact that a former pontiff and his successor wrote letters on the same issue within days of each other underlined the peculiarity of a situation in which, for the first time in centuries, two Popes live virtually under the same roof.
While Pope Francis lives in a Vatican guesthouse, his successor is living out his retirement in a former convent a few hundred yards away.
It is not known how often the two men meet.
Benedict's assertion that he had done what he could to end sexual abuse by priests was disputed by groups representing the victims of paedophile clergy.
EXPOSED
"Over a clerical career that lasted more than six decades, we can't think of a single child-molesting bishop, priest, nun, brother or seminarian that Benedict ever exposed," said Barbara Dorris of the US-based Survivors Network of those Abused by Priests.
"In the church's entire history, no one knew more but did less to protect kids than Benedict. As head of CDF, thousands of cases of predator priests crossed his desk. Did
he choose to warn families or call police about even one of those
dangerous clerics? No. That, by definition, is a cover-up."