"There was an attack against the armed forces chief, General Prime Niyongabo, but happily he was unharmed," Burundi's deputy police chief, General Godefroid Bizimana, told AFP.
He said two attackers were killed in the clash, and a third arrested. Another senior police source said four bodyguards were also killed, as well as a female police officer.
"Reinforcements have arrived. We are pursuing the remainder of the commandos," Bizimana.
Another senior police source, who asked not to be named, said the attack appeared to have been "meticulously prepared".
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Tensions remain high in the central african nation following President Pierre Nkurunziza's successful bid for a third term in power in July.
Nkurunziza won a highly-controversial third term in July in polls the United Nations said were not free or fair. His bid sparked an attempted coup and months of civil unrest led by opposition groups, who condemned his re-election bid as unconstitutional.
Many have raised alarm bells at the risk of renewed conflict in Burundi, which lies in the heart of central Africa's troubled Great Lakes region.
At least 300,000 people were killed in a civil war there which ran from 1993-2006.