The deaths came in an attack in the Kamenge district of Bujumbura yesterday.
Police director general General Andre Ndayambaje told AFP two officers were killed and one was wounded, while a local resident said a civilian also lost his life and two others were wounded.
A similar attack in the centre of the capital of the small central African nation wounded three policemen, the general said.
The local resident said the grenade attack was followed by automatic gunfire.
More From This Section
One policeman died on the spot and another was wounded in the legs, he said.
Minutes later, a grenade exploded under the car of the local police chief who had arrived on the scene. He got out but was killed by a shot.
According to the resident, a civilian was also killed in the shooting and a woman and a child wounded by the second grenade.