Williamson told Swedish television in an interview last year that he believed "there were no gas chambers".
"Williamson ... must in an absolutely unequivocal and public way distance himself from his positions regarding the Shoah"
He also said no more than 300,000 Jews died in Nazi concentration camps, rather than the six million accepted by mainstream historians.
Williamson later apologised to the pope "for the unnecessary distress" he caused him, but has not yet recanted his statements.
The Vatican said the pope was not aware of Williamson's denial of the Holocaust when the pontiff lifted excommunication orders on him and three other traditionalist bishops last month.
Williamson and the other three bishops were excommunicated 20 years ago after they were consecrated by the late ultraconservative Archbishop Marcel Lefebvre without consent from the then pope, John Paul II - a move the Vatican said at the time was an act of schism.
The Vatican said on Saturday that Benedict rehabilitated the four as part of his efforts to bring Lefebvre's Society of St Pius X back into the Vatican's fold.
Roman Catholic traditionalists reject most of the teachings of the Second Vatican Council. One of its key documents, "Nostra Aetate" (In Our Times) repudiated the concept of collective Jewish guilt for the death of Jesus Christ.
Since Williamson made his comments, one Italian member of the society said "gas chambers existed at least for disinfecting" and another called the late John Paul II a heretic for advancing relations with Jews.
Jewish leaders welcomed the Vatican statement but some expressed scepticism that Pope Benedict was unaware of Williamson's views.
Finally, the Vatican has taken responsibility for one of the worst blunders in recent history," said Rabbi Marvin Hier, founder and dean of the Simon Wiesenthal Centre.
"What is particularly astounding is the Vatican assertion that they didn't know about his Holocaust views. All somebody had to do was Google him and they would have found them," he added in a statement.
Elan Steinberg, vice-president of the American Gathering of Holocaust Survivors and their Descendants, said the Vatican's move "was the necessary step we have asked for in order to defuse the moral crisis caused by his readmission to the Church".
"The process can now begin of healing the deep wound that this crisis caused to the Catholic-Jewish dialogue."
Germany's Central Council of Jews said the Vatican's move was a positive signal and a reaction to a demand by Angela Merkel, the German chancellor, for "clarification" regarding the Vatican's demand for Williamson to publicly recant, adding it could lead to a resumption of ties with the church.
The council had said last week it was breaking off contact with the church over the controversy.