Police initially reported 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.

Italian authorities named the first two killed as Olga Raschietti, 83, and Lucia Pulici, 75, both Roman Catholic nuns.

But in the early hours of Monday morning, another nun in the same convent was killed, her body beaten and head hacked off. Colleagues named her as Bernadette Boggia, aged 79.

"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.

Pope Francis issued his condolences.

"The Holy Father begs the Lord to welcome into his kingdom of peace and light these three faithful and devout nuns," he said in a statement.

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.

Police spokesman Colonel Helmegilde Harimenshi said all three were raped.

Father Mario Pulcini, 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 that she had heard a noise in the convent.

'Barbarity'

"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.

Italian Foreign Minister Federica Mogherini condemned the attacks.

"Once again we are witnessing the sacrifice of people who, in total commitment, have spent their lives to relieve the suffering still on the African continent," she said.

The suspected killer in the first attack was seen fleeing the convent with a knife in his hand, said Damien Baseka, a local government administrator in Bujumbura.

Police sources suggested the third nun was killed by an accomplice who had hidden in the convent.

Police spokesman Colonel Helmegilde Harimenshi said three men were being questioned.

In 2011, a Croatian nun and an Italian charity worker were killed in an apparent botched robbery in northern Burundi.

The small nation in Africa's Great Lakes region emerged in 2006 from 13 years of brutal civil war and its political climate remains fractious ahead of presidential polls due in June 2015.