MEXICO CITY—Throughout Mexico’s drug war, the country’s military has shrugged off allegations that soldiers have occasionally tortured or even executed suspected members of drug cartels, saying that the majority of the charges were made up by zealous activists or the cartels themselves.

But three high-profile cases this month that are being investigated outside the military’s own secret courts have prompted the army’s top commander to say the military may have committed serious human-rights abuses.

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