Thousands of people have gathered in a tiny village in Switzerland to witness the ordination of four new Catholic bishops, in defiance of an appeal by Pope Leo XIV.

The four, one from the United States, one from Switzerland, and two from France, are members of the controversial Society of Saint Pius X (SSPX), also sometimes known as Lefebvrevites after SSPX's founder Marcel Lefebvre.

The Society rejects key modernising reforms introduced by the Vatican in the 1960s and 1970s, including permission to hold Mass in languages spoken by the congregation, rather than only in Latin.

Pope Leo made a last-minute appeal to SSPX leaders earlier this week not to proceed with the ordination, describing it as a "schismatic act", which could "tear the seamless garment of Christ".

But on Wednesday morning, under cool grey Alpine skies, the society defied the Pope – regarded by millions of Catholics as God's representative on Earth – and proceeded with the ordination.

At least 15,000 people gathered in Écône to watch hundreds of robed priests - carrying candles and crosses, and dispensing incense - progress through the village into a pasture where a large tent had been set up.

There, the four candidates for bishop prostrated themselves before an altar, their heads buried in red velvet pillows. Ceremonial organ music played, the ordination vows were taken, of course, in Latin.

But for these four men, their time as bishops may be very short.

The last time the Society ordained new bishops, in 1988, they were immediately excommunicated.

Although Pope Benedict XVI repealed the excommunication in 2009 in an unsuccessful attempt to heal the rift, Pope Leo is also expected to exclude the new bishops from the Catholic Church.

To some, the Vatican's objections to SSPX may seem exaggerated; after all, many Churches have separate branches, some more conservative than others. But ordaining bishops without the Pope's consent is regarded as a serious violation of the unity of the Church.

The split is not just about SSPX's desire to conduct Mass only in Latin.

The Society, founded by controversial French archbishop Marcel Lefebvre in 1970, has always wanted to preserve a kind of medieval mystique in which priests, bishops, cardinals, and the Mass itself are seen as somehow closer to God, and therefore separate from ordinary people.

SSPX has consistently defied the Vatican over multiple policies designed to make the Church more accessible and egalitarian, including establishing ties with other religions, recognising the right to religious freedom, and participating in debates over big social and political questions.

It even objected to the Vatican's decision to have priests face the congregation when holding Mass, preferring the medieval practice of facing the altar, with their backs to the congregants.

SSPX's Superior General, Davide Pagliarani, denied trying to sustain the rift, telling the congregation in Écône the ordination was taking place "precisely because we love the Pope as the vicar of Christ, as the head of the Church… we don't want to see the Pope humiliated any more, on the side of false shepherds representing false religions".

The defiance poses a challenge to Pope Leo, who is relatively new in post.

Although the Society is small, with an estimated 600,000 followers compared with the Catholic Church's more than 1.4 billion members, it is now represented in dozens of countries, including the US, where it has an enthusiastic following in Kansas.

And SSPX clearly has funds. The ordination was live-streamed on YouTube in seven languages.

The thousands who turned up to witness it were offered baseball caps commemorating "Écône2026". There were even novelty gift packs of Swiss wine, costing $92 (£80), each bottle labelled with a picture of a mitre, the bishop's crown-like hat.

So although Pope Leo has made it clear he views the new bishops as illegitimate, and their ordination as a clear attack on the Catholic Church, he may not want to do anything further to make his feared schism any worse.