The communiqué, issued today from the society's headquarters in Menzingen, Switzerland, added that "no public statement will be made before the audience."
The meeting between the Pope and Bishop Fellay was meant to be discreet, but was made public in a letter by one of the society's four bishops, Richard Williamson, who is opposed to any "compromise" with the Holy See.
The Holy See has yet to confirm this audience, but it has not denied the information published by the society, founded by French Archbishop Marcel Lefebvre.
Pope John Paul II stated in an 1988 apostolic letter, "Ecclesia Dei," that the "illegitimate" ordination of four bishops within the society by Archbishop Lefebvre constituted "a schismatic act."
The ordination cut short the attempt at an agreement between the Holy See and the society, carried out on behalf of John Paul II by Cardinal Joseph Ratzinger, then prefect of the Congregation for the Doctrine of the Faith and now Benedict XVI.
The bishops ordained by Archbishop Lefebvre were Swiss Bernard Fellay, Frenchman Bernard Tissier de Mallerais, Briton Richard Williamson and Argentine Alfonso de Galarreta.
Archbishop Lefebvre died in 1991 and was succeeded in the leadership of the society by Bishop Fellay.
In a recent interview with DICI, the press agency of the motherhouse of the Society of St. Pius X, Bishop Fellay announced that, if he were to meet with Benedict XVI, he would request two things.
First is the possibility for all priests to celebrate the Tridentine Mass without special permission from the local bishop, as is now required. Second is the "recanting [of] the decree of excommunication related to the consecrations" of the four bishops.