"So the attitude of the official church is what changed; we did not," he said. "We were not the ones who asked for an agreement; the pope is the one who wants to recognize us."

In 2009, Pope Benedict XVI lifted the excommunications that had been incurred by Bishop Fellay and other SSPX bishops when they were ordained without papal permission 11 years earlier. Also in 2009, the pope established a Vatican committee to hold doctrinal talks with society representatives.

In September 2011, the Vatican gave Bishop Fellay a "doctrinal preamble" outlining "some doctrinal principles and criteria for the interpretation of Catholic doctrine necessary to guarantee fidelity" to the formal teaching of the church. Neither the Vatican nor the SSPX has made the text public, but the Vatican said it leaves room for "legitimate discussion" about "individual expressions or formulations present in the documents of the Second Vatican Council and the successive magisterium" of the church.

Bishop Fellay submitted his first response to the document in March, but the Congregation for the Doctrine of the Faith, with the approval of Pope Benedict, defined it as "insufficient." The bishop gave the Vatican his second response in April and, as of June 7, it was still under study at the Vatican.

In the interview on the SSPX website, Bishop Fellay said, "We are still not in agreement doctrinally, and yet the pope wants to recognize us. Why? The answer is right in front of us: there are terribly important problems in the church today."

The reconciliation talks, he said, are a sign that the Catholic Church has begun to recognize it needs to recover traditions and traditional teaching eclipsed by the Second Vatican Council. If the SSPX were to reconcile fully with the church, Bishop Fellay said, its members would continue to denounce "doctrinal difficulties" in the church, but would do so while also providing "tangible signs of the vitality of tradition" in its growing membership and vocation rate.

Speaking to members of the SSPX who are wary of reconciliation, Bishop Fellay said "one of the great dangers is to end up inventing an idea of the church that appears ideal, but is in fact not found in the real history of the church."

"Some claim that in order to work 'safely' in the church, she must first be cleansed of all error. This is what they say when they declare that Rome must convert before any agreement, or that its errors must first be suppressed so that we can work," he said.

But the reality of the church's history shows that "often, and almost always, we see that there are widespread errors" and that God calls holy men and women to work within the church to correct the errors, Bishop Fellay said.

"We are being asked to come and work just as all the reforming saints of all times did," he said.

Bishop Fellay said he did not have a timetable for the conclusion of the talks. "There are even some who say that the pope will deal with this matter at (the papal summer villa in) Castel Gandolfo in July."