About 22 people, reportedly including children, were killed at Bourasso in Kossi province and 12 more were killed at Namissiguima in Yatenga province, officials and sources say.
The attack took place early in the morning at the nation's Namissiguima military base in the province of Sanmatenga.
The inauguration of Lt Col Paul Henri Sandaogo Damiba as president comes about three weeks after he led a military coup to overthrow elected head of state Roch Marc Christian Kabore.
The leaders previously issued a statement to say the bloc "firmly condemns" the coup, accusing the military of forcing Kabore to resign "under threat, intimidation and pressure".
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