"That this overlapping of two opposing processes took place and momentarily upset peace between Christians and Jews, as well as peace within the church, is something which I can only deeply deplore,'' he wrote.
He thanked "all the more our Jewish friends'' for understanding his commitment to friendship.
The pope's move to explain his actions and admit wrongdoing is highly unusual in the church's history.
"The letter is very personal, very anguished, very pained but very honest," said an Italian bishop who received it.
The pope said that the Williamson affair unleashed a storm of "vehemence" which hurt him deeply, saying he was saddened that even Catholics "thought they had to attack me with open hostility".
Reverend Federico Lombardi, a Vatican spokesman, said the letter was "really unusual and deserving of maximum attention".
Benedict angered Jewish leaders and many Catholics by lifting the excommunication of Williamson and three others in a bid to heal a 20-year-old schism within the church.
The schism began in 1988 when the four were ordained without Vatican permission.
World Jewish organisations and Angela Merkel, the German chancellor, had criticised the pope for rehabilitating the British bishop.