What is considered a war waged for a purported holy purpose?

The term that best fits the definition of a war waged for a purported holy purpose is "Holy War." This concept historically refers to conflicts that are justified by religious beliefs, where the participants view their struggle as divinely sanctioned or a conflict between good and evil. Examples include the Crusades, which were battles fought by Christians to reclaim the Holy Land, or jihad in some interpretations of Islamic doctrine.

In contrasting terms, "War on Faith" does not specifically denote a conflict waged under the guise of holiness; instead, it suggests an opposition to faith itself. "Sacred War" might seem similar, but it is less commonly used in contemporary discourse and can lack the broader recognition attached to "Holy War." "War of Peace" suggests intentions of promoting peace and does not align with the idea of a war justified by religious doctrine or purpose. Therefore, "Holy War" is the most accurate term for conflicts believed to have divine justification.