A total of 126 people were freed, 33 of them wounded, from the four-star Splendid hotel after security forces retook the facility and nearby Cappuccino restaurant today over 12 hours after the attack began, Interior Minister Simon Compaore told AFP.
The assault on the two venues, popular with Westerners and UN personnel, was crushed by midday but the police and military were still combing the area for other suspects, a security source said.
Compaore said "three jihadists - an Arab and two black Africans - have been killed". The security source said four jihadists were killed, two of them women, and the victims were of 18 nationalities.
Al-Qaeda in the Islamic Maghreb (AQIM) claimed the attack on behalf of an affiliate, saying the strike on the former French colony was in "revenge against France and the disbelieving West", according to a statement carried by US-based monitoring group SITE.
The attack will heighten concerns that jihadist groups are casting their net wider in search of targets in west Africa, two months after a siege at a luxury hotel in neighbouring Mali, where 20 people were killed, against mostly foreigners.
AQIM and Al-Murabitoun jointly claimed that attack.
President Roch Marc Christian Kabore, who took office just last month, a year after a popular uprising ousted longtime leader Blaise Compaore, called on his fellow citizens to show "courage".
The attack began around 7.45 pm when an unknown number of attackers stormed the 147-room hotel in the heart of Ouagadougou.
Another witness reported seeing four assailants.
The hotel and its environs were transformed into a battleground as Burkina Faso troops, backed by French forces based in the city under a regional counterterrorism initiative, launched an attempt to retake the hotel around 2 am.
The US, which has a small contingent in the country, said it supported French forces in the operation.
Several guests managed to escape from the hotel through side entrances, including Labour Minister Clement Sawadogo, who emerged unscathed.
"It was horrible, people were sleeping and there was blood everywhere. They were firing at people at close range," Yannick Sawadogo, one of those who escaped, told AFP.
Compaore, the interior minister, told AFP that 10 bodies had been discovered on the terrace of the Cappuccino restaurant.
The foreign ministry in Paris confirmed a Frenchwoman was among the injured but said no French nationals had yet been confirmed among the victims.
French President Francois Hollande denounced the "odious and cowardly attack", with the European Union and Britain issuing similar condemnations.
Also today, Burkina's interior ministry reported that two foreigners were kidnapped Friday in the northern Baraboule region, near the border with Niger and Mali.
The ministry said the couple were Austrian, though the Austrian foreign ministry was unable to immediately confirm the report.
The attack in Ouagadougou was unprecedented in Burkina Faso and comes as people were enjoying a return to stability after the election which ended a shaky transitional period following Compaore's ouster.
"The elections went off well...That makes the country a symbol of progress, which is what those people want to destroy," Cynthia Ohayon, a security analyst with the International Crisis Group said.
Al-Murabitoun had already begun to move into the impoverished country of around 17 million. In April last year, the group claimed the abduction of the Romanian security chief of a mine in the country's north.