The head of the Society of St. Pius X says the breakaway traditionalist group is on the verge of giving a definitive response to the Vatican's offer of re-unification.

"All ambiguity has now been resolved among us. Very soon we will convey to Rome the position of the Chapter," Bishop Bernard Fellay said July 16, following the conclusion of the society's general chapter in Econe, Switzerland.

The society has spent the past month considering a June 13 offer from the Vatican's Congregation for the Doctrine of the Faith that would give the traditionalist group personal prelature status within the Church.

A personal prelature is a Church jurisdiction without geographical boundaries designed to carry out particular pastoral initiatives. At present, the only personal prelature in the Church is Opus Dei.

In return, the society would have to agree to certain doctrinal statements, including, it is presumed, an acceptance of the documents of the Second Vatican Council.

Bishop Fellay said all the documentation relating to his Vatican negotiations was put before the Society's General Chapter between July 9 and 14. The gathering brought together the 40 most senior figures in the organization to decide on Rome's offer.

"This made it possible for us to conduct direct discussions which have cleared out the doubts and dissipated any misunderstandings, resulting in peace and unity of hearts, which of course is something to rejoice about," he said.

The July 2 appointment of Bishop Gerhard Muller as the new Prefect of the Congregation for the Doctrine of Faith seems to have become a significant stumbling block for Bishop Fellay. He believes the former bishop of Regensburg "does not like" the society, which has a seminary in the bishop's former diocese, and said that he treated them "like lepers" even after Pope Benedict XVI lifted the excommunication on the society's four bishops in 2009.

"He is the one who stated that our seminary should be closed and that our students should go to the seminaries of their dioceses of origin, adding bluntly that 'the four bishops of the SSPX should resign,'" recalled Bishop Fellay.

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The Society of St. Pius X was founded in 1970 by the Frenchman Archbishop Marcel Lefebvre in response to errors he believed had crept into the Catholic Church following the Second Vatican Council.

The society has had a strained relationship with the Church since its founder ordained four bishops against the will of Pope John Paul II in 1988.