A reprisal is a limited and deliberate violation of the laws of war to punish an enemy for breaking the laws of war. A reprisal is not an atrocity. In the United States military, the lowest ranked commander who can authorize a reprisal is the theater commander (i.e. Europe, Middle East, etc).
A related concept is Letter of marque (license to hunt enemy ships and retake lost ships from the enemy).
... appeared in Italian (Venice, 1488,
Milan 1489), Spanish (Seville, 1536), Arabic (Rome,
1663), Armenian (Rome, 1674), Hebrew (Frankfort,
1837), and ...