The government said the attack on the military headquarters was a suicide vehicle bombing and that a regional antiterrorism meeting may have been the intended target. The 5,000-member force combines troops from Burkina Faso, Mali, Niger, Chad and Mauritania, with France leading the efforts to raise worldwide funding.
French special forces helped to kill the assailants at the French embassy, security minister Sawadogo said.
Visiting the headquarters on Saturday, Prime Minister Paul Kaba Thieba said he saw "apocalyptic scenes" and condemned "with the utmost severity this terrorist attack, cowardly, which attacks our country, once again, which sows death, unnecessary destruction". He was not able to give further casualty details.
Smoke rises amid one of the attacks in Ouagadougou.
In a phone call that day to President Roch Marc Christian Kaboré, UN Secretary-General António Guterres expressed solidarity with the country's Government, according to a statement issued by his spokesperson.
At the same time, the bomb went off near the headquarters of the Burkinabe armed forces and the French cultural center, other witnesses said.
The embassy was attacked around 10:15am on Friday, with witnesses at the nearby state TV offices saying the attackers arrived in a pick-up truck, shouted, "Allahu akbar!" and began shooting.
The attack on the army headquarter was aimed at a conference room, narrowly missing a meeting of top officers, which would have "beheaded" the military leadership, according to Security Minister Clement Sawadogo.
"Perhaps it was the target. In any case the room was literally destroyed by the explosion", the minister said.
The G5 Sahel's completed force are to be composed of 5,000 troops and aims to be fully operational by the end of the month.
In reprisal for Burkina Faso's participation in a regional fight against Islamist militant.
A Reuters reporter saw an ambulance entering the army compound.
No group claimed responsibility for Friday's attacks.
France has a military presence in Burkina Faso as part of Operation Barkhane, which was launched in 2014 to combat jihadist activity across the Sahel region.
Burkina Faso is one of the poorest countries in the world.
Last August, suspected extremists killed at least 18 people last August during a raid on a restaurant in Ouagadougou and militants have targeted Burkinabe security forces along its remote northern border region with Mali. In response to the new violence in eastern Burkina Faso, troops from Burkina Faso and nearby Mali and Niger have increased patrols.
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