"Vengeance can wipe out an entire generation," he said, in an address to the nation on Sunday, urging calm.
According to BBC, a presidential spokesman said it was too early to blame anyone for the killing of Gen Adolphe Nshimirimana in a rocket and gun attack on his car.
Mr Nkurunziza won a third term last month, amid deadly protests over his decision to run for office again.
Opponents argued this contravened the constitution and there was a failed coup attempt in May.
The attackers reportedly targeted the general's car with machine guns and rocket launchers in the Kamenge district of the capital Bujumbura. BBC reports.
Presidential spokesperson Gerve Abehayo rejected suggestions that the attack could have been carried out by elements within Burundi's own security apparatus, after witnesses reported four men in military uniform spraying the general's car with bullets.
Meanwhile, President Nkurunziza has called for an investigation into the general's killing to be concluded within a week.