The group has just released a statement, and CNS has details:
The breakaway traditionalist Society of St. Pius X said unresolved “doctrinal difficulties” with the teachings of the Second Vatican Council and the Catholic Church’s subsequent liturgical reform could lead to a “new phase of discussions” over possible reconciliation with Rome.
The society released its statement June 14, a day after the Vatican presented its superior general, Bishop Bernard Fellay, with an evaluation of the society’s position on a series of doctrinal questions and a draft document proposing that the society become a personal prelature.Bishop Fellay, who was accompanied by an assistant, met with U.S. Cardinal William Levada, prefect of the Congregation for the Doctrine of the Faith, Archbishop Luis Ladaria, congregation secretary, and Msgr. Guido Pozzo, secretary of the Pontifical Commission “Ecclesia Dei.”
The SSSPX statement said that Bishop Fellay listened to Cardinal Levada’s “explanations and clarifications” and offered the cardinal an explanation of the “doctrinal difficulties” that Vatican II and the subsequent reform of the Mass present for the traditionalists.
“The desire for further clarifications could lead to a new phase of discussions,” the SSPX said.