It said the dead were mostly African migrant labourers, including from Niger, Chad and Sudan, who were working in local artisanal gold mines.
"This attack against civilians demonstrates the ongoing chaos and failure of these military governments," it said in a statement.
Burkina Faso's military government did not immediately respond to a request for comment.
Neither Mali nor Wagner have said how many troops they lost in the recent clashes, though Wagner did say the commander of its unit in the area, Sergei Shevchenko, was among the dead. Russian military bloggers estimated 20 or more Wagner personnel had been killed.
The CSP said it had killed and injured dozens of Malians and Russians, while an Islamist group affiliated with al Qaeda said it had killed 50 Russians and 10 Malian soldiers.
Mali, Burkina Faso and Niger, all former Western allies that have pivoted towards Russia since their militaries took power in coups, signed a mutual defence pact last year, which Mali invoked to explain Burkina Faso's role in the air strikes.
The Tuareg live in the Sahara desert, which includes parts of northern Mali. Many complain of marginalisation by the Malian government.
Tuareg separatists launched an insurgency against Mali in 2012, demanding an independent homeland called Azawad. Their struggle later became entangled with an al Qaeda-aligned Islamist rebellion in the same region.
Published 31 July 2024, 12:38 IST