Nkurunziza, who was re-elected last month, said in a televised address that he has ordered the police to find Lt Gen Adolphe Nshimirimana's killers within 10 days.
The killing of Nshimirimana who was the senior presidential adviser for internal security could spark revenge killings and further fuel violence that stemmed from Nkurunziza's controversial bid for a third term.
Nshimirimana was killed in a drive-by shooting early yesterday in the capital, Bujumbura after which a gunfire rang out last night.
"Despite or perhaps because of his brutal reputation, Adolphe was generally seen as untouchable, with no one in a position of power daring, or even suggesting, holding him to account," she said.
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Human Rights Watch has received frequent allegations that he was behind many incidents of killing, torture, arrests of suspected opponents and other abuses over the past several years, she said.
The US has condemned the killing and is urging restraint. Nkurunziza won the July 21 presidential polls with 69 percent of the vote. The international community condemned the elections as not credible because of violence, intimidation, media restrictions and questions over the legitimacy of a third term for Nkurunziza.