ROME — Officials of the Congregation for the Doctrine of the Faith met with representatives of the Society of St. Pius X (SSPX) on Tuesday for two hours at the Vatican to discuss matters of Church teaching.

“During the meeting, various problems of a doctrinal and canonical nature were examined, and it was decided to proceed gradually and over a reasonable period of time in order to overcome difficulties and with a view to the envisioned full reconciliation,” the Holy See Press Office stated Sept. 23.

The meeting, described as cordial by both sides, involved from the Congregation for the Doctrine of the Faith: its prefect, Cardinal Gerhard Müller; its secretary, Archbishop Luis Ladaria Ferrer; its adjunct secretary, Archbishop Augustine Di Noia; and Archbishop Guido Pozzo, secretary of the Pontifical Commission Ecclesia Dei.

The representatives of the Society of St. Pius X were its superior general, Bishop Bernard Fellay; Father Niklaus Pfluger, first assistant general; and Father Alain-Marc Nely, second assistant general.

The meeting was the first between Cardinal Müller and Bishop Fellay since the cardinal was appointed prefect.

A press release from the SSPX said the meeting’s goal was “to allow Cardinal Müller and Bishop Fellay to meet for the first time and to discuss together the status of the relations between the Holy See and the Society of St. Pius X.”

“During this cordial meeting, doctrinal and canonical difficulties were discussed, and the current situation of the Church was mentioned,” the statement continued. “It was decided to continue the discussions in order to clarify the points of contention that remain.”

The Society of St. Pius X was founded by Archbishop Marcel Lefebvre in 1970 to form priests, as a response to what he described as errors that had crept into the Church following the Second Vatican Council. Its relations with the Holy See became strained in 1988, when Archbishop Lefebvre consecrated four bishops without the permission of Pope John Paul II.

The illicit consecration resulted in the excommunication of the five bishops; the excommunications were lifted in 2009 by Benedict XVI, and since then, negotiations between the society and the Vatican have continued, in order “to rediscover full communion with the Church.”

In remitting the excommunications, Benedict also noted that “doctrinal questions obviously remain, and until they are clarified, the society has no canonical status in the Church, and its ministers cannot legitimately exercise any ministry.”

The biggest obstacle for the society’s reconciliation has been the teaching on religious liberty in Vatican II, which it claims contradicts previous Catholic teaching.

In January, 2013, Archbishop Di Noia wrote to the society’s priests, seeking “reconciliation and healing” and telling them that “some new considerations of a more spiritual and theological nature are needed … considerations that focus rather on our duty to preserve and cherish the divinely willed unity and peace of the Church.”

As Pope Benedict XVI stated in 2009, “Until the doctrinal questions are clarified, the society has no canonical status in the Church, and its ministers — even though they have been freed of the ecclesiastical penalty — do not legitimately exercise any ministry in the Church.”