Italian prosecutors have begun an inquiry into the death after a miscarriage of a woman of 32 who was pregnant with twins.
The family of Valentina Milluzzo said the doctor treating her refused to abort the foetuses because he was a "conscientious objector" to abortion.
The hospital involved has categorically rejected the family's claims.
The woman's burial has been postponed while further investigations are carried out.
Milluzzo was admitted to Cannizzaro hospital in the Sicilian city of Catania on 29 September after suffering complications and going into premature labour in her 19th week of pregnancy. She had had fertility treatment at another health centre.
She was in a stable condition in hospital for more than a fortnight but on 15 October her blood pressure dropped and her condition worsened.
According to the family's lawyer, one of the foetuses was suffering breathing problems. The lawyer alleges that the gynaecologist refused to abort the foetuses in order to save the mother and said: "As long as it's alive, I will not intervene."
No action was taken while the troubled foetus was still alive and hours later both were stillborn, the lawyer said.
Overnight, the mother's condition deteriorated and she contracted an infection. On 16 October she was transferred to intensive care, where she died.
Angelo Pellicano, the head of the Cannizzaro hospital, said the lawyer was wrong.
"There was no conscientious objection on behalf of the doctor that intervened in this case because there was no voluntary termination of the pregnancy, but (the miscarriage) was forced by the grave circumstances," he told the Ansa news agency. "I rule out that a doctor could have told the family what they say he told them."
Sources told Ansa that the doctor had not been registered as a "conscientious objector".
Catania's prosecutor has halted Milluzzo's burial while a post mortem examination is carried out. There are unconfirmed reports that some of the hospital's medical staff may be investigated.
A senior doctor at the hospital, Paolo Scollo, told the Corriere website that all the doctors in his department were "objectors", and external doctors were called in when necessary. "However, in this case we're talking about a spontaneous miscarriage, no external help was needed. So we do not think the doctor was negligent," he said.