The Society of St Pius X has announced in a communiqué that it will not seek reintegration with the Church, accusing pastors, including Pope Francis, of doctrinal errors.
Bishop Bernard Fellay, Superior General of the Society, made the announcement following a three-day meeting at Anzère in Switzerland.
"In the great and painful confusion that currently reigns in the Church," Bishop Fellay writes, "the proclamation of Catholic doctrine requires the denunciation of errors that have made their way into it and are unfortunately encouraged by a large number of pastors, including the Pope himself.
"The Society of Saint Pius X, in the present state of grave necessity which gives it the right and duty to administer spiritual aid to the souls that turn to it, does not seek primarily a canonical recognition, to which it has a right as a Catholic work," he continues.
Insisting that the Society will redouble its efforts to spread the "social reign of Christ," Bishop Fellay says this cannot happen "without the support of a Pope who concretely favours the return to Sacred Tradition."
Bishop Fellay also promises prayer and penance for the Pope in order "that he might have the strength to proclaim Catholic faith and morals in their entirety."
The Society was founded by the late Archbishop Marcel Lefebvre in 1969, in the wake of Vatican II.
It opposed the Council's modernising reforms, the introduction of Mass in the vernacular, and outreach to Jews and other Christians.
The Vatican in 2014 resumed reconciliation talks after doctrinal discussions launched under Emeritus Pope Benedict XVI collapsed. The society said yesterday its primary aim wasn't legal recognition but restoring Catholic tradition to the Church.
Last September, Pope Francis surprised many by extending an olive branch to the group by decreeing that during his Holy Year of Mercy anyone who confesses their sins to a priest of the society will be considered validly forgiven, Crux reports.
In April, after a private meeting with Francis, Bishop Fellay said the Pontiff had promised to extend this recognition indefinitely.
However, Bishop Fellay also said that Pope Francis is "totally atypical" and a man hard to pin down in the "usual categories."
"I would say one of the major problems we have is that the normal way of judging someone is by his actions and conclude, 'He's acting like this because he thinks like that.' So [we] go back to a doctrine or sometimes an ideology," he said in a May interview.
Communiqué from Bishop Fellay (Society of St Pius X)
Breakaway Catholic group accuses Pope of spreading errors (The Washington Post)