The Priestly Fraternity of St Pius X announced on Monday that Bishop Bernard Tissier de Mallerais is now out of danger.
According to the statement, the bishop fell on Saturday after the Angelus prayer in the community's seminary in Econe and lost consciousness. He suffered a fractured skull with internal haemorrhaging.
However, his condition has since stabilised. He is not yet able to communicate, but is gradually coming out of his induced coma.
The hospital staff are optimistic, "but his condition remains serious and the consequences of the trauma are uncertain". The Society of St Pius X is asking for the prayers of the faithful for the bishop.
Fraternity of St Pius X not in communion with the Church
Born in France in 1945, Tissier de Mallerais was ordained a bishop in 1988 by Archbishop Marcel Lefebvre (1905-1991) without the Pope's permission, together with three other priests of the Society of St Pius X.
The Vatican Congregation for Bishops subsequently excommunicated Lefebvre and the four bishops he had consecrated.
Excommunication is one of the highest church penalties. Among other things, those subject to this penalty may not receive or administer the sacraments and may not hold any ecclesiastical office.
Pope Benedict XVI had the excommunication of the four living bishops lifted in 2009.
The Society of St Pius X rejects most of the reforms of the Second Vatican Council (1962-1965).
The main points of contention are the liturgy, religious freedom and ecumenism.
To this day, the Society of St Pius X is therefore not in full communion with the Catholic Church.
All of its clerics are suspended, which means they are not allowed to assume or exercise ecclesiastical offices.
As the Society of St Pius X has no legal status in the Church, it relies on its own bishops to confer ordinations.
Most recently, deacons and priests were ordained in June at the community's seminary in Zaitzkofen, Bavaria.
As in previous years, Bishop Rudolf Voderholzer of Regensburg , in whose diocese the seminary is located, had expressly forbidden ordinations.