VATICAN CITY (RNS) In a bid to end a decades-long split in the Catholic Church, the Vatican offered a conservative breakaway group a special status enjoyed only by the Opus Dei movement.

Cardinal William Levada

The offer came during a meeting on Wednesday (June 13) between the head of the Vatican doctrinal office, Cardinal William Levada, and Bishop Bernard Fellay, superior general of the Society of St. Pius X (SSPX). It was announced on Thursday.

The status, known as a “personal prelature,” would allow the SSPX to operate directly under the pope’s authority, without territorial boundaries.

The SSPX rejects the modernizing reforms of the Second Vatican Council (1962-1965), including church acceptance of ecumenism and its rejection of anti-Semitism. The group officially split from the Catholic Church in 1988, when its founder, Archbishop Marcel Lefebvre, ordained four bishops without papal consent.

Ever since his election in 2005, Pope Benedict XVI has tried to reconcile with the SSPX. In 2009, he lifted the excommunication of the four traditionalist bishops and started doctrinal talks with the group. Jewish groups were outraged after one of the bishops, Richard Williamson, turned out to be a vocal denier of the Holocaust.

According to the Vatican chief spokesman, the Rev. Federico Lombardi, before the SSPX can be granted a status within the church, it must sign a doctrinal agreement with the Vatican whose text has been under discussion since last September.

During Wednesday’s meeting, Levada submitted to Fellay the final draft of the agreement, and he is expected to respond “within a reasonable lapse of time,” according to a Vatican statement. “The ball is in their court now,” said Lombardi.

But the SSPX on Thursday hinted that a “new phase” of talks may be needed.

Divisions over a potential reconciliation with Rome have been growing within the SSPX in recent months, and will probably be addressed during the group’s general assembly in early July.