The first two Catholic nuns killed were identified as 83-year-old Olga Raschietti and 75-year-old Lucia Pulici but in the early hours of Monday, the body of another nun was discovered, her body beaten and head hacked off
Three elderly Italian nuns were reported to have been sexually assaulted and murdered in twin attacks in their convent in the capital of Burundi.
The police say a manhunt has been launched for their killers.
It was reported by the police initially that two nuns were stabbed to death on Sunday afternoon. The killer then battered one of the two with a rock, before fleeing the convent.
The first two Catholic nuns killed were identified as 83-year-old Olga Raschietti and 75-year-old Lucia Pulici but in the early hours of Monday, the body of another nun was discovered, her body beaten and head hacked off.
She was identified by her colleagues as 79-year-old Bernadette Boggia.
"After the discovery of the two nuns who were brutally killed... the decapitated body of the third nun was found," Deputy Director General of Police Godefroid Bizimana told AFP.
According to the diocese of Parma in Italy, they were killed during a botched burglary attempt.
But Burundi's police said the motive of the killing was not clear, pointing out that no money was taken.
Father Mario Pulicini, an Italian Catholic priest working in the same parish, said after the first two nuns were killed, Boggia had called him in the middle of the night reporting she had heard a noise in the convent.
"The body of Sister Bernadette was found lying in a pool of blood, her head decapitated, and her face bore signs of beating," he told AFP in shock.
"The perpetrators had abused her, as they had violated the other two sisters earlier."
Burundian Vice-President Prosper Bazombanza said the government was "appalled by such barbarity", and promised police would do all they could to arrest the killers.
"No one can understand how a third sister was killed late at night... Burundi's government promises to shed light on this matter as quickly as possible," he added.
Police spokesman Colonel Helmegilde Harimenshi said three men were being questioned.