Vatican City, Apr 4, 2016 / 11:04 am (CNA/EWTN News).- Both the Vatican and the Society of St. Pius X have confirmed that this weekend Pope Francis met with the priestly society's superior general, Bishop Bernard Fellay, at the Vatican.

The Holy See press office issued a statement April 4 indicating that Pope Francis and Bishop Fellay had met April 2 at the Vatican.

An April 4 statement issued by the SSPX, meanwhile, said that Pope Francis received Bishop Fellay at his Domus Sanctae Marthae residence in the Vatican on April 1. The statement said Bishop Fellay was accompanied by Fr. Alain-Marc Nely, second assistant general of the priestly society.

“Pope Francis had wanted a private and informal meeting, without the formality of an official audience. It lasted 40 minutes and took place under a cordial atmosphere,” the SSPX stated. “After the meeting, it was decided that the current exchanges would continue. The canonical status of the Society was not directly addressed, Pope Francis and Bishop Fellay having determined that these exchanges ought to continue without haste.”

The statement from the priestly society added that on April 2, Bishop Fellay met with Archbishop Guido Pozzo, secretary of the Pontifical Commission Ecclesia Dei – the Vatican office of the Congregation for the Doctrine of the Faith responsible for doctrinal discussions with the SSPX.

The SSPX 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, “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 statements on religious liberty in Vatican II's declaration Dignitatis humanae, which it claims contradicts previous Catholic teaching.

Doctrinal discussions between the SSPX and the Congregation for the Doctrine of the Faith broke down in the summer of 2012, when the society's superior general, Bishop Bernard Fellay, would not sign a doctrinal preamble presented by Rome. Talks between the CDF and the society resumed, however, in 2014.

Since then several moves have suggested a warming in relations between the Vatican and the SSPX.

In 2015 the Holy See delegated a cardinal and three bishops to visit the seminaries of the SSPX. They were sent to become better acquainted with the society, and to discuss doctrinal and theological topics in a less formal context.

And Pope Francis announced in a September 2015 letter on the Jubilee Year of Mercy that during the jubilee year the faithful can validly and licitly receive absolution of their sins from priests of the SSPX.

“I trust that in the near future solutions may be found to recover full communion with the priests and superiors of the Fraternity,” he wrote.