Eight armed forces personnel were killed in the fighting in the West African nation on Friday, the government said, while a French security source said 12 more were seriously injured.
Eight attackers were also killed and 80 people, including civilians, were wounded, officials said.
The government said the attack on the military HQ was a suicide car bombing and that a regional anti-terrorism meeting may have been the intended target.
Visiting the HQ 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”.
The Group to Support Islam and Muslims (GSIM) claimed to have carried out the twin attacks, in a message cited by Mauritania’s Al-Akhbar news agency.
Led by the Malian jihadist Iyad Ag Ghaly, the group is allied to al-Qaeda and has claimed responsibility for previous attacks in the troubled Sahel region.
GSIM said the Ouagadoudou attacks were a response to the deaths of some of its leaders “in a French army raid in northern Mali two weeks ago,” the agency reported.
According to French military sources, some 20 jihadists were “killed or captured” on that occasion.
– ‘Terror attack’-
Authorities on Saturday began to gather clues at the two attack sites.
The car bomb explosion left a huge crater in the pavement by the military HQ and a hole in the side of the building, with windows smashed and bullet holes in the walls.
“This is a terrorist attack, linked to a current or another terrorist movement in the Sahel… or to others who want to are destabilise or block our democratic progress,” said communication minister Remis Fulgance Dandjinou on Saturday morning.
Two people were arrested near the military HQ, a security source told AFP.
“It was a panic yesterday (Friday). People were running around in the city, trying to get home. Shops were closing, schools too,” said Sayouba Ouedraogo, a 36-year-old driver.
A salesman who usually sells cigarettes in front of the French Embassy, Zondi Mahamadi, 52, said it was chaos: “People ran, they left everything, even motorcycles, bikes, we climbed a fence to get away.”
“Does religion command people to kill? Religion has never said that,” he added.
– Soft targets to hard targets –
The violence began mid-morning Friday when heavy gunfire broke out in the centre of the Burkinabe capital.
Witnesses said five men armed with Kalashnikov assault rifles got out of a car and opened fire on passersby before heading towards the French embassy.
They were “dressed in civilian clothes” with their faces uncovered, witnesses said.
At the same time, the bomb went off near the headquarters of the Burkinabe armed forces, about a kilometre (half a mile) from the site of the first attack.
A gunman who attacked the military HQ was wearing the uniform of the national army, according to a security source.
Officials from Burkina Faso, Chad, Mali, Mauritania and Niger had gathered at the HQ for a G5 Sahel meeting, an anti-jihadist group which aims to train 5,000 troops and be fully operational by the end of the month.
The location of the meeting was changed at the last moment, Security Minister Clement Sawadogo said.
Four attackers were shot outside the French embassy and another four at the military HQ, another security source told AFP.
“After soft targets, such as hotels and restaurants, this attack aimed at hard targets, strong symbols,” Paul Koalaga, a security consultant in Burkina Faso said, adding there appeared to be “a problem at the intelligence level”.
– Previous attacks –
Burkina Faso has been the target of jihadist attacks since 2015, and this is the third time in two years that Ouagadougou is the target of jihadist attacks targeting places frequented by Westerners.
On August 13 last year, two assailants opened fire on a restaurant on the capital’s main avenue, killing 19 people and wounding 21. No one has so far claimed responsibility for it.
On January 15, 2016, 30 people — including six Canadians and five Europeans — were killed in a jihadist attack on a hotel and restaurant in the city centre.
GSIM also claimed responsibility for a February 21 attack near the border with Niger which left two French soldiers dead and a third injured in an area which is believes to shelter jihadists.
Bank security guard Alassane Sawadogo on Saturday criticised the government for the security situation. “The government only has to negotiate with the jihadists, if they don’t want to have to fight them”.
“We’re fed up and tired,” he added.