Conte said that as a lawyer by training and a Catholic, while he had no doubt about the right to life, he was not so sure about the right to die.
He was speaking to the newspaper after the constitutional court ruled on Wednesday that assisted suicide could be lawful, despite a law forbidding it in Italy.
“To choose to be taken towards death and to ask help from personnel for that, who must be specialised — there some doubt is permitted,” said Conte.
“And if one did get to that, one would have to at least recognise a conscientious objection for anyone who did not feel capable (of taking part),” he added.
Wednesday's court ruling stressed that assisted suicide could only concern patients with incurable conditions who were being kept alive artificially and whose physical and psychological suffering was judged to be unbearable.
The patients concerned would also have to be fully capable of taking such a decision freely and consciously, the court added.
The court also made it clear that its decision had been taken in the expectation that parliament would make the relevant changes to existing law.
Italy, which has a strong Catholic tradition, currently forbids euthanasia, and has laws punishing instigating or assisting suicide with up to 12 years in prison.
A number of European countries have laws permitting assisted suicide under strictly regulated conditions, but contentious cases still come before the courts.
Earlier this month in the Netherlands, the first country to legalise euthanasia, a court acquitted a doctor over the euthanasia of a woman with severe dementia.
The case attracted media attention due to details of how the unnamed patient was given a sedative in her coffee but nevertheless had to be restrained by her family as the now-retired doctor injected the euthanasia drug.