A final assessment given by the same government source showed that seven members of the security forces were killed, nine assailants neutralised and more than 80 people were left injured from the attacks.
This is the third major assault on Ouagadougou in the past two years.
Gunfire and explosions resounded for hours, subsiding by midday.
The insurgency has caused thousands of deaths, prompted tens of thousands to flee their homes and dealt crippling blows to economies that are already among the poorest in the world.
Witnesses said five men armed with Kalashnikov assault rifles got out of a auto and opened fire on passersby before heading towards the French embassy. Witnesses at the nearby state TV offices told The Associated Press that the attackers had arrived in a pickup truck, shouted, "Allahu akhbar!" and began shooting.
The government said eight soldiers were killed, as well as eight assailants - four at the embassy and four at military headquarters.
French government sources said there were no French casualties and described the situation in Ouagadougou as "under control".
"Some of the soldiers ran into a nearby bank to seek shelter".
Souro Sanou, an official at the hospital in the capital, said that several people have been wounded.
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Fico accused the opposition Wednesday of using the murder as a "political tool to get people out on the streets and gain power". A candlelit protest in the capital Bratislava called by an opposition party drew around 1,000 people Wednesday night.
Ouagadougou has been attacked by Islamic extremists targeting foreigners at least twice in the past few years. In 2016 and 2017, the terrorists chose to attack hotels and restaurants popular among foreigners. But experts say the terror threat in Burkina Faso is increasingly homegrown.
No group claimed responsibility for Friday's attacks.
"In these hard moments, I would like to reaffirm to Africa and the entire world my unshakeable faith in the capacity of the Burkinabe people to preserve their dignity and ferociously oppose their enemies", Kabore said in a speech on national television.
Among his objectives has been ending the use of French, the former colonizer's language, in regional schools.
According to French military sources, some 20 jihadists were "killed or captured" on that occasion.
The government said the attack on the military was a suicide auto bombing and that a planned meeting of the G5 Sahel regional anti-terrorism force might have been the target. The troops support forces in Burkina Faso, Chad, Mali, Mauritania and Niger against groups such as the Defense Group of Islam and Muslims.
The countries' troops join forces where they can.
There was no immediate claim of responsibility.