WASHINGTON—Recently declassified U.S. interrogation reports shed new light on one of Iraq’s most prominent Shiite political figures and Iran’s role in training and arming Iraqi militias that attacked U.S. troops during the Iraq war.

The interrogations of Qais al-Khazali resonate today because he leads a major Shiite militia group whose power has grown after recent elections in Iraq, where the U.S. and Iran are jostling for influence.

Mr....