The memo also noted that there are members of the Church's hierarchy who are sympathetic to them, but that they can only collaborate after regularization, and that the SSPX will need new bishops in the future and that licit consecration should be pursued.
In its conclusion, the text argues that if "God wants to come to the effective aid of His Church, which is bleeding from a thousand wounds, he has thousands of different means of doing so. One of these is the official recognition of the SSPX through the Roman authorities." It then closes with a prayer for the intercession of the Virgin Mary.
It has been speculated that the normalization of the SSPX would be accomplished by recognizing the group as a "personal prelature," a canonical structure which so far has only been used for Opus Dei.
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 particularly strained in 1988 when Archbishop Lefebvre and Bishop Antonio de Castro Mayer consecrated four bishops without the permission of Pope John Paul II.
The illicit consecration resulted in the excommunication of the six bishops; the excommunications of the surviving bishops were lifted in 2009 by Benedict XVI, and since then, negotiations "to rediscover full communion with the Church" have continued between the Society and the Vatican.
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 obstacles for the Society's reconciliation have been the statements on religious liberty in Vatican II's declaration Dignitatis humanae as well as the declaration Nostra aetate, which it claims contradict previous Catholic teaching.
Archbishop Pozzo addressed this issue in his discussion with La Croix, saying that he considers Nostra aetate as "directives for pastoral action, directions, and suggestions or exhortations of a practical pastoral nature," adding that "the acceptance of the texts on relations with other religions is not a prerequisite for the canonical recognition" of the SSPX.
"The difficulties raised by the SSPX concerning the Church-State relationship and religious freedom, the practice of ecumenism and dialogue with non-Christian religions, certain aspects of the liturgical reform and its concrete application, remain subject to discussion and clarification but do not constitute an obstacle to a canonical and juridical recognition of the SSPX," the Vatican official said.
The archbishop noted that following the canonical regularization of the Society, the declarations of Vatican II will "remain subject to discussion and deeper study, in order to obtain greater precision and avoid the misunderstandings or ambivalences that we know to have spread throughout today's ecclesial world."
Under Pope Francis 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.
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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.
And Bishop Fellay met with Pope Francis and Archbishop Pozzo April 1-2. Bishop Fellay indicated that at that meeting, the Pope had said the SSPX is Catholic and he would not condemn it, and that he wishes to extend the faculties of its priests.