Piergiogio Welby's widow, who defended the doctor's decision, said the family would hold a lay funeral for him on Sunday if the church denied rites. Anti-euthanasia campaigners and some right-wing newspapers have described Welby's death as murder.
"For me it was not a murder, absolutely. Piero died naturally, falling asleep and giving back his soul to the creator," Mina Welby said.
Welby's family said they learned of the Rome diocese's decision to withhold a religious funeral when they tried to make arrangements with their local parish.
"I won't deny that I was furious," said his sister, Carla. She said the decision would be particularly hard for her mother.
"I don't know with what words we will tell her that she can't hold a funeral for her son in church," she said.
The Vatican -- which maintains a strong influence on Italian politics -- vehemently opposes euthanasia, insisting that life must be safeguarded from its beginning to its "natural" end, but says that extraordinary means need not be used.
In many apparent suicides, the Church allows funerals on the assumption that the deceased was not of sound enough mind to make rational decisions. The office of the Vicar of Rome said it had refused a religious funeral for Welby because of his "repeated and publicly affirmed" desire to "end his life."
Cardinal Javier Lozano Barragan, a senior Vatican official in charge of health-care issues, said Wednesday that if doctors determined that the respirator constituted extraordinary means, it could be removed, in line with Vatican teaching.
Welby, 60, who was terminally ill with the degenerative disease muscular dystrophy, died Wednesday after a long campaign which included writing a book and pleading with Italy's president to be allowed to die.
"He wanted to carry on the issue of euthanasia; his fear was having to die in a terrible way, suffocated," said Mina Welby. "He didn't think only about himself, but about many other ill people ... who would have this problem at the end of their lives."
Rome prosecutors have begun investigating Welby's death and have questioned, as a witness, Mario Riccio, the doctor who sedated Welby and disconnected his respirator.
The case has highlighted an apparent contradiction in Italian law: Patients have a constitutional right to refuse treatment, but the Italian medical code requires doctors keep a patient alive.
On Saturday, a Rome judge recognized Welby's right to refuse treatment -- but ruled there is no law that could force a doctor to take measures that would lead to a patient's death, even at the patient's request.
The judge urged legislators to address the contradiction, saying the decision to disconnect a respirator "is left to the complete discretion of any doctor to whom the request is made."
Mina Welby said her husband could not come to terms with diminishing mental faculties that made it difficult for him to read and write.
"He could not accept to just lie there and watch television and listen to some music," she said. "For him life meant being able to move, to move also with the brain, and he couldn't do that anymore."
Monsignor Rino Fisichella, who has close ties to the Vatican, told state TV that those who suffer should seek mercy through prayer, but in Welby's case, "it was repeatedly asked, in an explicit way, that this life be taken," leading church officials to deny the funeral, said Fisichella, who is rector of the Pontifical Lateranense University in Rome.
He said that the church "must proclaim yet again the joy of life and the capacity to give sense to life and to suffering."