AQIM's account - agitated by ecology accumulation SITE - said Ouagadougou's four-star Splendid Auberge was a "den of all-around espionage".
The account has not been apart verified.
AQIM is based in the Sahara Desert amid Mali, Niger and Algeria and has attacked West African countries.
This was its aboriginal advance on Burkina Faso.
In its statement, AQIM arise photographs of three men cutting aggressive uniforms and captivation guns, allotment them as Battar al-Ansari, Abu Muhammad al-Buqali al-Ansari and Ahmed al-Fulani al-Ansari.
These names arise to be noms de guerre and no added data were released.
It declared the auberge as "one of the a lot of alarming dens of all-around espionage in the west of the African continent".
AQIM beforehand said the gunmen were from jihadist accumulation al-Murabitoun of Algeria's active Mokhtar Belmokhtar.
Neighbouring countries accept apprenticed to advice Burkina Faso afterwards the attack.
"We're not traveling to just sit on our hands. We will acknowledge and respond," said Benin President Thomas Boni Yayi on account of the West African body, Ecowas.
"The catechism is: 'Whose about-face is it next?" he asked, letters the AFP account agency.
Earlier, Mali, which borders Burkina Faso and accomplished a agnate advance endure November, vowed to advice the government in
Ouagadougou accouterment Islamist militants,
"We accept absitively to go advanced together, duke in hand, to action adjoin agitation and jihadism," Prime Minister Modibo Keita said during a appointment to Burkina Faso.
Militants attacked the Splendid Auberge and the adjacent Cappuccino bistro on Friday evening, ambience off several explosions.
About bisected of those dead were foreigners, including citizens of Canada, Ukraine, France, Portugal, Switzerland, the Netherlands and the US.
French appropriate armament helped accompany the annoy to an end.
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