Two of the sources said 28 people were killed and a third spoke of "around 30" dead in the attack in the capital Ouagadougou.
In a simultaneous attack, the French embassy was also targeted.
Burkinabe security sources gave a lower toll, saying "around 15" people were killed, while the army's medical chief, Colonel Amado Kafando, said 75 others had been injured. It was unclear whether these figures applied to one or to both attacks.
French government sources said there had been no French casualties and described the situation as "under control".
Speaking to state TV channel RTB, Information Minister Remis Fulgance Dandjinou said the attack had "strong overtones of terrorism".
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