Burundi's government on Saturday ordered "insurgents" to end weeks of demonstrations against President Pierre Nkurunziza's third term bid and ordered all barricades to be removed within 48 hours.

"The protesters and organizers of this insurrection must immediately and unconditionally stop this insurrection that handicaps the life of Burundi and its people," the National Security Council said in a statement read out in Bujumbura.

Authorities in Burundi arrested a leading dissident and shut down the main independent radio station Monday as they battled a second day of demonstrations against a bid by the president to cling to power for a third term.

The army was also deployed around the capital Bujumbura, after at least two people were shot dead during clashes with police in the capital Bujumbura and after two further deaths were reported overnight in alleged attacks by ruling party militia.

Two protestors have been shot dead during clashes with police in the capital of Burundi, witnesses said on Sunday.

Clashes were taking place in several parts of Bujumbura the day after the president launched a controversial bid to stay in power for a third term and despite a government ban on protests.

Three elderly Italian nuns were sexually assaulted and murdered in twin attacks in their convent in the capital of Burundi, police said Monday as a hunt was launched for their killers.