Other attacks in the region, which have occurred over the past month, include the abduction of 110 schoolgirls in Nigeria on February 19, and Wednesday's attack that killed four United Nations peacekeepers in Mali.
The government said eight soldiers were killed, as well as eight assailants - four at the embassy and four at military headquarters.
There was no immediate claim of responsibility for the attack, which is the third major assault on Ouagadougou in just over two years.
Burkina Faso's Army Chief of Staff Headquarters and French embassy in Ouagadougou on Friday were hit by vehicle bomb attacks, which left 16 people dead and over 90 injured, the Minister of Security Clement Sawadogo was quoted as saying.
Witnesses said five armed men got out of a auto and opened fire on passersby before heading towards the French embassy.
Its members "expressed their solidarity with Burkina Faso in its fight against terrorism and stressed the need to intensify regional and global efforts to combat terrorism and violent extremism, which may be conducive to terrorism". Northern areas near the border with Mali have been a regular target of attacks by various extremist groups, some of them vowing to step up deadly assaults in response to the recent deployment of a regional G5 Sahel force.
Government spokesman Remi Dandjinou told Reuters on Saturday that arrests had been made in connection with the attacks but it was unclear if he was referring to new arrests or the two that authorities had reported on Friday.
At the same time, the bomb went off near the headquarters of the Burkinabe armed forces and the French cultural centre, about a kilometre (half a mile) from the site of the first attack, other witnesses said. But experts say the terror threat in Burkina Faso is increasingly homegrown.
According to French military sources, some 20 jihadists were "killed or captured" on that occasion. "Targets could include hotels, restaurants, police stations, customs offices, military posts, and schools".
The Ouagadougou prosecutor's office appealed for witnesses "to assist in the search and identification of accomplices, hosts and any possible facilitators" of the events.
That meeting had been moved to a different room, otherwise the death toll could have been far higher. "In any case the room was literally destroyed by the explosion", the minister added.
The G5 forces will be comprised of approximately 5,000 soldiers, which will be fully operational by the end of March.
It has already carried out operations against terrorists with help from the French army. The 5,000-member force combines troops from Burkina Faso, Mali, Niger, Chad and Mauritania, with France leading the efforts to bring in worldwide funding.
The French Embassy came under attack around 10:15 a.m. Friday.
The insurgency in the region 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.