Eight of those who died were security officers and 49 people were captured, Col Gaspard Baratuza said.
Residents in the capital earlier said the bodies of some 34 men were found on the streets – and accused police of taking revenge. It is not clear if that number is included in the army’s total.
Unrest has hit Burundi since April.
There have been continued protests since President Pierre Nkurunziza announced his decision to seek a third term in office, which he won in a disputed election in July.
Friday saw some of the worst violence since the unrest began. Officials described heavily armed attackers launching co-ordinated early morning assaults on army installations in three areas – Ngagara, Musaga and Mujejuru.
Fighting could then be heard throughout the day and sporadic gunfire continued overnight.
Residents said dozens of men were rounded up as their homes were raided, and many of their bodies were found on the streets of the capital on Saturday morning.
The largest number of bodies were found in Nyakabiga district, a focus of anti-government protests. Others were discovered in the southern neighbourhood of Musaga.
One witness told the AFP news agency that some of the victims were “kids” and had been shot execution-style “through the top of the skull”.
BBC Africa analyst Richard Hamilton says bodies on the streets are almost a daily occurrence in Bujumbura but this was by far the largest number of deaths in one night.
Col Gaspard Baratuza, giving details of the final toll, said that “79 enemies” were killed, “45 captured and 97 weapons seized and on our side eight soldiers and policemen were killed and 21 wounded”.
According to the UN, at least 240 people have been killed since April and more than 200,000 have fled to neighbouring countries.
There have been regular killings of both opposition activists and Nkurunziza supporters.
The violence has raised fears of a return to worsening ethnic tension between Hutus and Tutsis.
Mr Nkurunziza led a Hutu rebel group against the then Tutsi-dominated army during the civil war that followed the killing of Hutu President Melchior Ndadaye in 1993.