The Vatican spokesman, the Rev. Federico Lombardi, said Bishop Richard Williamson's views had no impact on the decision to lift the excommunication decree.
The pope's decision by no means implies "sharing (Williamson's) ideas or his comments, which will be judged on their own," the ANSA news agency quoted Lombardi as saying.
Lefebvre founded the Swiss-based Society of St. Pius X in 1969, opposed to the liberalizing reforms of the 1962-65 Second Vatican Council, particularly its allowing of Mass to be celebrated in local languages instead of Latin.
The four bishops were excommunicated in 1988 after Lefebvre consecrated them without Rome's consent. Lefebvre was excommunicated as well.
In a statement Saturday, the current head of the society and one of the rehabilitated bishops, Bernard Fellay, expressed his gratitude to Benedict and said the decree would help the whole Catholic Church.
The Society believes the Church is in crisis and blames in part the doctrinal reforms of Vatican II, including its ecumenical outreach, for causing it.
"Our Society wishes to be always more able to help the pope to remedy the unprecedented crisis which presently shakes the Catholic world," Fellay said.
Benedict made clear from the start of his pontificate that he wanted to normalize relations with the society, meeting within months of his election with Fellay and convening cardinals to discuss bringing the society back into the Vatican's fold.
In 2007, Benedict answered one of Fellay's key demands by relaxing restrictions on celebrating the old Latin Mass. In lifting the excommunication decree, he answered the society's second condition for beginning theological discussions about normalizing relations.
In lifting the decrees, Benedict risked a new clash with Jews, who had already been incensed by the rehabilitation of the old Latin Mass because it contained a prayer calling for their conversion.
