Witnesses at the national television office which faces the French Embassy said that five people came in a pick-up truck in front of the embassy and started shooting after saying "Allahu Akhbar" and then set fire to the truck and began shooting.
Barricades were erected to keep people from that area and from the French Embassy and the prime minister's office in the eastern part of the city center where gunfire and smoke were reported.
Reuters reported that an aide to France's Foreign minister Jean - Yves le Drian said France's embassy and cultural institute in the capital are no longer in danger.
In 2016, al-Qa'eda in the Islamic Maghreb claimed responsibility for an attack on a hotel that claimed the lives of 30 people.
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He was on the National Security Council from 2001 to 2003 during the administration of former President George W. News and others reported the story on Thursday, citing multiple sources.
In a separate development on Friday, the specialist U.S. website SITE, which monitors extremists activity, said kidnappers had released a video of a 75-year-old French hostage, Sophie Petronin, who had been abducted in northern Mali in late 2016.
Three security sources, two in France and one in West Africa, told AFP that at least 28 people were killed in the attack on the military headquarters alone.
Four attackers were also "neutralized" and two Burkina Faso security members killed at the French Embassy, according to Dandjinou.
French government sources said there were no French casualties and described the situation in Ouagadougou as "under control".
Burkina Faso, like other countries in West Africa, has been targeted sporadically by jihadist groups operating across Africa's Sahel region.
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Among his objectives has been ending the use of French in regional schools. 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 the bloodshed in response to the recent deployment of the G5 Sahel force.
Five countries - Burkina Faso, Niger, Chad, Mali and Mauritania - launched a new task force past year to tackle Islamist militants in the arid Sahel region, to which worldwide donors have committed $500 million US. But the terror threat in Burkina Faso is increasingly homegrown, experts say.
"Our country was once again the target of dark forces", President Roch Marc Christian Kabore said in a statement.
During the 2016 assault, security forces waited for hours before trying to intervene.
An attack by gunmen past year on a restaurant in Ouagadougou left at least 18 people dead, including two attackers.
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