Three people were killed on Friday in grenade attacks on police in Burundi where nearly 600 people have been arrested during protests and clashes sparked by the president's bid to stay in power.

The director general of police, General Andre Ndayambaje said two officers were killed and one was wounded in the attack in Kamenge district of the capital Bujumbura, while a local resident said a civilian also lost his life and two others were wounded, according to The Telegraph on Saturday.

A similar attack in the centre of the capital of the small central African nation wounded three policemen, the general said.

A senior police officer, who requested anonymity, said "It is clear that the demonstrators launched the simultaneous attacks".

"If they want war, they will get war," he said.

The political unrest erupted after the ruling CNDD-FDD party last weekend designated President Pierre Nkurunziza as its candidate in the next presidential election, which is due to be held on June 26.

Opposition figures and rights groups say Nkurunziza's attempt to stand for a third consecutive term violates the constitution as well as a peace deal that ended a civil war in 2006.