In a formal communique published after the meeting, the Vatican said it wanted to "avoid an ecclesial rupture with painful and incalculable consequences," so Bishop Fellay and leaders of the society were asked to further clarify their response to a "doctrinal preamble" the Vatican asked them to study last September.

The text of the preamble was not made public, but the Vatican had said it "states some doctrinal principles and criteria for the interpretation of Catholic doctrine necessary to guarantee fidelity" to the formal teaching of the church, including the teaching of the Second Vatican Council.

Bishop Fellay delivered the society's official response in January, the Vatican said, and it was "placed under the examination of the Congregation for the Doctrine of the Faith and successively under the judgment of the Holy Father."

"In compliance with the decision of Pope Benedict XVI," the communique said, Bishop Fellay was given a letter signed by Cardinal Levada explaining that "the position he had expressed is not sufficient to overcome the doctrinal problems that are at the basis of the fracture between the Holy See and the society."

Father Lombardi said Cardinal Levada told Bishop Fellay the society had a month to clarify its position in order to heal "the existing fracture."

"A further clarification from the society is expected by mid-April," said Father Lombardi. The society has been given "more time for reflection to see if some further step can be made."

The Vatican spokesman would not give examples of the points on which the Society of St. Pius X and the Vatican still differ since the original preamble was never published. He said the additional month given to the society shows "the case is not closed," although the letter to Bishop Fellay makes clear that the consequence of "a non-acceptance of that which was foreseen in the preamble" would be "a rupture, something very serious for the church."

Father Lombardi said Pope Benedict has taken many steps "to make possible a reconciliation" with the traditionalist group, including lifting the excommunications imposed on Bishop Fellay and other SSPX bishops, establishing a Vatican committee for doctrinal talks with society representatives in 2009 and drafting the "doctrinal preamble" to explain the "minimal, essential" elements on which the society would have to agree for full reconciliation.

"A response was expected, it was not sufficient and, so, now (the Vatican is saying), 'If you think there is something else you would like to clarify, if you'd like to reflect some more to clarify your position, there is another month for you to do so,'" Father Lombardi said.

In late November, Bishop Fellay had said, "This doctrinal preamble cannot receive our endorsement, although leeway has been allowed for a 'legitimate discussion' about certain points of the (Second Vatican) Council."

When the Vatican's doctrinal discussions with the society began in 2009, both sides said the key issues to be discussed included the concept of tradition in general, as well as the Second Vatican Council's teaching on the liturgy, the unity of the church, ecumenism, interreligious dialogue and religious freedom.