Gen Adolphe Nshimirimana was killed when men in a car shot at him and his bodyguards while traveling in the Kamenge neighbourhood, Willy Nyamitwe told The Associated Press today.
The attackers also lobbed a grenade into Nshimirimana's vehicle, and the general was evacuated before he later died from his wounds, he said.
The killing is likely to stoke tensions in Burundi, which has been wracked by violence since April when it was revealed that Nkurunziza would seek a third term in office.
Nshimirimana was widely seen as a key member of the president's security team who helped to put down an attempted coup in May.
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Nkurunziza won the July 21 presidential polls with 69 percent of the vote while his closest rival, Agathon Rwasa, got 19 per cent.
The international community condemned the elections as not being credible because of violence, intimidation, media restrictions and questions over the legitimacy of a third term for Nkurunziza.
Many fear that Nkurunziza's determination to stay in power can trigger widespread violence in the poor central African country of 10 million that has a history of civil strife.