Kazakhstan is treading delicately as it strives to keep two feuding neighbors happy amid a row over Russia’s accidental shoot-down of an Azerbaijani civilian airliner, which crashed outside the Kazakh city of Aktau. Kazakh officials have little to gain and a lot to lose as they oversee the crash investigation.

Azerbaijan’s President Ilham Aliyev said on Sunday that the Azerbaijani airliner that crashed in Kazakhstan on Wednesday, killing 38 people, was shot down by Russia, albeit unintentionally. Aliyev told Azerbaijani state television that the aircraft was ...