However, a statement released by the Swiss-based society July 1 implied that the traditionalist group did not accept all the conditions set out in the letter, and it appealed to Pope Benedict XVI to lift the 1988 decree of excommunication against the society's bishops who were ordained without papal permission.
The Vatican press office said July 3 that it did not plan to comment on the statement.
In the July 1 statement, the Society of St. Pius said, "The very general - not to say vague - character of the demands singularly contrasts with the urgency of the ultimatum," adding that they appeared to be geared simply to promoting dialogue rather than resolving differences.
The memorandum was given June 4 to the head of the society, Bishop Bernard Fellay, by Cardinal Dario Castrillon Hoyos, the Vatican official in charge of dialogue with the traditionalists.
In addition to asking for a response by the end of June, the memo set four other conditions for a move toward full reconciliation:
• To respond with the same generosity shown by the pope.
• To avoid public comments showing a lack of respect toward the pope or which could "be negative for ecclesial charity."
• To avoid "the pretext of a magisterium superior to the Holy Father" and to not present the society in opposition to the church.
• To demonstrate the will to act honestly in full ecclesial communion and with respect for the pope's authority.
The society's July 1 statement said Bishop Fellay responded to the ultimatum with a June 26 letter to Pope Benedict and that "Cardinal Castrillon Hoyos acknowledged receipt of the letter the next day."
In a June 28 interview with an Italian-language radio station in Switzerland, Bishop Fellay said, "It is false to say (my response was a) total rejection" of the Vatican's conditions.
"Rather, I see in this ultimatum something very vague, confused. But I have responded and it has to be seen how Rome will react," he said.
Bishop Fellay said, "It is possible that now there will be a little more coldness" in the discussions with the Vatican, but the society wants to continue its dialogue with the rest of the church.
"We do not want to break with the church. Our greatest desire is to be fully accepted," he said. "This is also for the good of the church, because you can see the church has serious problems and we know that we have the solution. We are not innovators; we simply follow what the church has always done and which worked in the past."
Asked whether he risked permanently closing the possibility of reconciliation by not accepting all the Vatican's conditions, Bishop Fellay said: "For me, this ultimatum makes no sense. We have a relationship with Rome that is unfolding with a certain rhythm, which, it is true, is slow. But it also is true that the cardinal (Castrillon) and the Holy Father would like to see an accelerated rhythm."
Last year, Pope Benedict widened the possibility for use of the Tridentine rite, the form of Mass used before the Second Vatican Council. That was a long-standing request of the society.
But Bishop Fellay has continued to criticize the Vatican on other matters, and has expressed his society's continued opposition to several teachings of Vatican II, especially in the areas of ecumenism and religious freedom.
In April Bishop Fellay said the time was not right for reconciliation with the Vatican, because church leaders have not taken steps to reverse the "crisis" introduced by Vatican II.
One source said the new Vatican offer signaled that the Vatican was not willing to continue dialogue with the traditionalist society indefinitely.
The society broke with the Vatican in 1988 when its founder, the late French Archbishop Marcel Lefebvre, ordained four bishops against papal instructions; Bishop Fellay was one of those ordained.
At that time, the Vatican said those involved in the ordinations were excommunicated.
Jesuit Father Federico Lombardi, Vatican spokesman, explained to French television July 2 that, while the four bishops were excommunicated, the priests of the society are validly ordained and the laity who attend their Masses are considered Catholics.
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