Police in Burundi say they have arrested a man suspected of killing and raping three elderly Italian nuns who were murdered in twin attacks on their convent.

"The suspected murderer of the three sisters is in our hands," Colonel Helmegilde Harimenshi said, adding the suspect had "confessed," Agence France-Presse reported.

The suspect reportedly acted alone, Harimenshi said.

The man arrested, who was not named, was found with a key to the convent and a mobile telephone belonging to one of the nuns, AFP reported citing police sources.

"All three of the murdered Italian nuns had serious health conditions , but all three, almost stubbornly, wanted to be buried in Burundi, a mark of love to the end," Fides news agency learned from Sister Delia Guadagnini.

She is the former Regional Superior of the Xaverian Missionary Sisters of Mary for Democratic Republic of Congo and Burundi.

The three nuns were named as Olga Raschietti, 83, Lucia Pulici, 75, and Bernadetta Boggian, aged 79.

Sister Delia said, "The three nuns returned to the parish agreeing to take on lighter tasks, because poor health prevented them from their former activities.

"Totally at the service of the people, making home visits, helping the poor the sisters were greatly loved by the people."

She added, "We cannot understand. In Burundi there was never any misunderstanding and we cannot imagine who would want to hurt us in such an evil manner. What happed is a tragedy and a mystery."

Father Mario Pulcini, superior of the Xaverian Missionaries in Burundi, reported the death of the three and told Vatican Radio that given the brutality of the attack, it seemed like some sort of vendetta or something more personal.

Pope Francis sent a message addressed to Archbishop Evariste Ngoyagoye of Bujumbura and to Sister Giordana Bertacchini, Superior General of the Xaverian Missionary Sisters of Mary, joining in prayer for the suffering of their families.

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

"Deeply saddened by the tragic death of the Xaverian Missionary Sisters killed in Burundi, the Holy Father wishes to assure his heartfelt participation in the profound suffering of the congregation for the loss of such dedicated sisters," said Francis.

He hoped, "that the blood they have shed may become the seed of hope to build true fraternity between peoples."

The Pope imparted "the comfort of his apostolic blessing" to their "families, the entire institute and those who mourn their loss."

Burundi's Vice-President Prosper Bazombanza said the government was "appalled by such barbarity."