The vicar-general of the Transalpine Redemptorists, Father Michael Mary, reported this month on the group's blog that "our community now truly rejoices in undisputed and peaceful possession of communion with the Holy See because our priests are now in canonical good standing."
He said that he had asked the Holy See, in the presence of the members of the Pontifical Commission Ecclesia Dei, for the priestly suspensions to be lifted.
The status of the Society of St. Pius X has been clouded since its founder, Marcel Lefebvre, gave episcopal ordination without permission to four priests. Pope John Paul II explained in a 1988 apostolic letter that "such disobedience -- which implies in practice the rejection of the Roman primacy -- constitutes a schismatic act."
The current leader of the Society of St. Pius X, Bernard Fellay, was one of the priests ordained by Lefebvre, who thus incurred excommunication.
The Transalpine Redemptorists are based on Papa Stronsay, an island in Orkney, north of Scotland.
Father Michael Mary went on to say: "We are very grateful to our Holy Father Pope Benedict XVI for issuing, last July, the 'Motu Proprio Summorum Pontificum' which called us to come into undisputed and peaceful communion with him.
"Now we have that undisputed communion! It is a pearl of great price; a treasure hidden in the field; a sweetness that cannot be imagined by those who have not tasted it or who have not known it, now for many years.
"Its value cannot be fully expressed in earthly language and therefore we hope that all traditional priests who have not yet done so, will answer Pope Benedict's call to enjoy the grace of peaceful and undisputed communion with him."
Father Michael Mary asked for prayers as the group seeks canonical erection. Originally based in Joinville, France, these Redemptorists eventually relocated to the Isle of Sheppey, Kent, and ultimately established themselves permanently at Papa Stronsay.
The Transalpine Redemptorists recently established a second monastery in the city of Christchurch, New Zealand. The blog of that monastery also reports the news of communion with the Holy See.
Their rule is based on that of St. Alphonsus Liguori, but they are not linked to the hierarchy of the Redemptorist order.