The Vatican said Tuesday that reconciliation talks are gradually resuming with a breakaway group of traditionalist Catholics following a two-year lull.

The head of the Vatican’s doctrine office, Cardinal Gerhard Mueller, met for three hours with the head of the schismatic Society of St. Pius X, Bishop Bernard Fellay.

A Vatican statement said they discussed doctrinal and legal problems, and that both sides agreed to “proceed gradually and over a reasonable amount of time” to examine their differences “with a view to the envisioned full reconciliation.”

The late Archbishop Marcel Lefebvre founded the society in 1969, opposed to the Second Vatican Council’s introduction of Mass in the vernacular and outreach to Jews. In 1988, the Vatican excommunicated Lefebvre and four bishops after he consecrated them without papal consent.

Emeritus Pope Benedict XVI had made reconciling a priority, liberalizing the use of the old Latin Mass which the society celebrates, removing the excommunications and enduring heated criticism when one of the rehabilitated bishops was shown to have denied the Holocaust. But three years of doctrinal talks collapsed in 2012 after Fellay refused to accept a core set of doctrinal demands required by the Holy See.

Relations worsened with the appointment of Mueller, who as bishop had called for the society’s seminary in his German diocese to close. Mueller pointedly refers to the group as having caused a “schism” in the church, something the society and its supporters deny.

The election of Pope Francis hasn’t improved matters. Francis doesn’t care for the old Latin Mass and has described traditionalists as self-absorbed retrogrades who aren’t helping the church’s mission to evangelize.

The society has been equally critical of Francis.