Pio Lieta, 86, suffered a fatal heart attack during an early-morning service at the Church of the White Madonna last Sunday.
An ambulance was called, and Mr Lieta, whose name means "pious" in Italian, was pronounced dead at the scene.
However, instead of halting the Mass, Father Mario Peron asked for the body to be covered with a white cloth and left Mr Lieta in the nave of the church while he finished the service.
It is against Italian law to move a body without the authorisation of a local magistrate.
"What could I have done?" said Fr Peron afterwards. "The Holy Mass has to be celebrated. It is not right to make an exception for one individual. Only people who do not understand the point of Mass would not understand the logic of my decision. We could not stop. We were united together in church and we prayed for him."
Only a handful of parishioners were present for the early-morning service, and some expressed their surprise at the priest’s decision to L’Adige, the local newspaper.
"We should have stopped as a sign of respect," said one unnamed worshipper.
Mr Lieta’s funeral took place at the same church today, and his family said they were not upset by what had happened.
Father Angelo Lieta, his son and a missionary in Chile, said: "My father would have agreed with the continuation of the Mass. I am only sorry I could not have been there myself."
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