The Society is planning to ordain more priests and deacons
A breakaway group of Roman Catholic traditionalists has ordained three men as priests, defying the Vatican.
The Society of St Pius X (SSPX), which split from the Vatican in 1988, argues that ordinations are necessary as the Church is facing a decline in clergy.
In January this year, Pope Benedict XVI revoked the 21-year excommunication of four bishops in the Swiss-based group.
But the Vatican said the society still had no status in the Church and any ordinations would be illegitimate.
Despite the warning from Rome, the SSPX went ahead on Saturday with the ordination of three men from Poland, Switzerland and Sweden at a ceremony held in Latin in Zaitzkofen in Germany.
The SSPX is also planning to ordain priests and deacons in Switzerland and the US.
The Pope's decision to lift the excommunications was an attempt to prevent a wider rift with the traditionalists of the SSPX, says BBC religious affairs correspondent Robert Pigott.
But it provoked an angry reaction as one of the bishops, British-born Richard Williamson, had cast doubt on the number of Jews who died in the Holocaust.
The Diocese of Regensburg in Germany, where Saturday's ordinations took place, also said the Pope's actions did not constitute permission to create new clergy.
But the SSPX said it had not been told to stop ordinations. The sect's spokesman in Germany, Father Andreas Steiner, said ordinations were justified given the "terrible emergency" faced by the Roman Catholic Church as its clergy and congregations declined.
"The Church is bleeding to death," he said.
SSPX was founded by a French archbishop, Marcel Lefebvre, in 1970 as a protest against the liberal reforms of the Second Vatican Council.
It says it has almost 500 priests as members and is active in more than 60 countries.