The Society of St. Pius X or SSPX, which broke with the church in 1988 by consecrating four bishops, rejects much of the work of the Second Vatican Council of 1962. But Bishop Bernard Fellay, the superior general, recently wrote the other bishops in the group, urging them to accept a dialogue with the church, Der Spiegel reported.
"You cannot know how much your attitude over the last few months -- quite different for each of you -- has been hard for us," he said.
Pope Benedict XVI had told the group that it must produce a clarification of its doctrinal differences with the Vatican. A Vatican spokesman, the Rev. Federico Lombardi, said Fellay's response has been "encouraging."
Other bishops have been more obdurate, Der Spiegel said, especially Richard Williamson, Williamson, an Englishman, became controversial in 2009 with his views about Judaism.
Williamson described Jews as "enemies of Christ" and blamed them and Freemasons for corrupting the Catholic Church. He also called "Protocols of the Elders of Zion" as accurate history and said the Nazis did not kill millions of Jews in gas chambers during World War II.