BRUSSELS—As 29 passengers sat aboard a Zurich-bound flight here Monday evening waiting for the last bags to be loaded, gunmen wearing police uniforms raced up to the plane and stole more than 120 packages of diamonds worth at least $50 million, and possibly much more.

Some of the eight masked robbers stood in front of the Helvetic Airways jet plane with machine guns, pointing laser sights at the pilots, while others forced ground workers to open the plane's cargo doors, according to Belgian prosecutors and other people familiar...