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Pope Benedict XVI has reinstated four bishops from an archconservative breakaway wing of the Roman Catholic Church, a decision that is bound to stir controversy within his own flock. But Saturday's announcement that the Vatican will undo the 20-year schism between the Vatican and the so-called Lefebvrian movement is all the more sensitive because it comes only days after the broadcast of an interview in which British-born Bishop Richard Williamson, one of those Benedict is bringing back into the fold, denies that the Nazi Holocaust ever happened.

"I believe there were no gas chambers," Williamson said. The bishop, who has been accused of anti-Semitism in the past, declared that the historical evidence was "hugely against" the accepted belief that close to 6 million Jews were systematically exterminated as part of Adolf Hitler's Final Solution. Williamson claims that no more than 300,000 Jews died during World War II. (See pictures of the Pope in France.)

The Vatican made no mention of those remarks in the communiqué that announced the papal decree that revokes the 1988 excommunication of Williamson and his three fellow bishops. Papal spokesman Father Federico Lombardi said the decree in no way means the Pope, a German, shares Williamson's views on the Holocaust.

Earlier this week, Jewish leaders warned that relations between the Holy See and Judaism would deteriorate if the controversial prelates were brought back into mainstream Catholicism.

The four bishops belong to a movement founded by the late French traditionalist Archbishop Marcel Lefebvre. Followers oppose dialogue with other religions and say Jews should convert. Rome's chief rabbi said Williamson's rehabilitation in particular would open a "deep wound" in Jewish-Vatican relations, which had already been strained by recent controversy over the effort to make Pope Pius XII a saint despite some historians' contention that he did little to save Jews during the Holocaust. The French Jewish organization CRIF called Williamson a "despicable liar whose only goal is to revive the centuries-old hatred against Jews."

Officially dated Jan. 21 (by coincidence the same day the interview aired), the decree states that the Pope "was inspired in this decision by the wish that complete reconciliation and full communion is reached as soon as possible." A senior Vatican official told TIME the Pope is expected to make the Society of St. Pius X (SSPX), the name Lefebvre followers call their movement, into a personal prelature of the papacy, the same special status that conservative lay group Opus Dei was granted by John Paul II.

Benedict's decision marks a watershed. Following on the Pope's 2007 decision to widen the use of the old Latin-rite mass, the rapprochement with the traditionalist faction appears to be a purely papal initiative. Beyond one or two retired Cardinals, few had been urging an end to the schism. The Society of St. Pius X itself had not budged from its hard line.

Some will hail Benedict as a bold defender of the rights of traditionalist Catholics and a man of conviction unbent by the winds of controversy, but others, both inside and outside the church, will take his embrace of the Lefebvre followers as the final proof that Benedict, deep down, is determined to make the church far more traditional than it is today.

Inside the Vatican, mainstream conservative voices have expressed consternation at the Pope's focus on reaching out to a group that includes some members (though not the four bishops) who don't even recognize papal authority. A Vatican official who has worked with the Pope going back to his Cardinal days said reconciliation with Lefebvre's followers "was dear to the heart of the Holy Father." Benedict is himself fond of traditional liturgy and felt that the four men were Catholics in good faith and should be allowed to call themselves Catholic.

According to the Vatican official, Benedict circumvented standing procedure "in cases of schism and heresy" that calls for consultation with the doctrinal Congregation office that he himself used to lead. "There wasn't the consultation as there normally is in these cases," the official says. "There was much perplexity in the Congregation." He added that in cases of revoking an excommunication, there must be a "concrete act of faith" to demonstrate obedience to the church's teachings and authority. The official Vatican statement cited a letter by Lefebvre's successor, Bishop Bernard Fellay, stating that the group has always considered themselves obedient Catholics.

Lefebvre founded his movement in 1970 in an effort to oppose the reforms of the Second Vatican Council, which had introduced the mass in local languages, encouraged dialogue with other religions and generally attempted to reconcile the church with modernity. In 1988, Lefebvre consecrated four bishops in defiance of the orders of Pope John Paul II and was automatically excommunicated, along with the new bishops he'd chosen as future leaders of his movement.

The group's website says it has members in 30 countries, with 463 priests and seminaries in Switzerland, Germany, France, the U.S., Argentina and Australia. It remains unclear how these long-disaffected followers of Lefebvre will be integrated into the church's hierarchy. "The Pope wishes to see this brought to an end," a second Vatican official told TIME. "But what's going to happen? These guys are bishops, and bishops take appointments from the Pope. Will they be obedient to what the Holy Father wants to do with them?" That's not the only question likely to arise in the coming days.

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• Jeff Israely