UN Secretary General Ban Ki-moon has condemned the killings of at least 11 people, including a UN staff member, in shootings and grenade attacks in the Burundian capital Bujumbura this week.

Several apparently targeted killings have been reported in recent months in the central African nation, which slid into crisis in April when President Pierre Nkurunziza's plan to remain in office for a third term triggered weeks of protests and a failed coup.

The spokesman for Ban said in a statement on Thursday that among the latest victims was a staff member of the Geneva-based International Organization for Migration. He called for investigations.

"The Secretary-General condemns the killing of nine civilians and two police officers in Bujumbura on October 13, amid exchanges of heavy gunfire in several neighbourhoods of the city," the statement said.

"The civilians, including a staff member of the International Organization for Migration, Evariste Mbonihankuye, were reportedly shot at close range."

Several people were killed on Tuesday in Ngagara, a neighbourhood of Bujumbura where opposition to Nkurunziza is strong. Local people said a television cameraman working for the state-run RTNB television and his family were among the dead.

Residents of the capital report frequent shootings and blasts, particularly in areas where there were protests before the July 21 presidential election.

Nkurunziza won the poll, which the opposition boycotted, but tensions have remained high in Bujumbura with frequent clashes between security forces and residents in anti-Nkurunziza strongholds.

This week's killings have also drawn condemnation from the regional body the International Conference on the Great Lakes Region and the US Embassy in Bujumbura.