The Algerian army stormed a natural-gas complex deep in the Sahara desert Saturday, ending a lethal and often chaotic four-day siege by suspected Islamist militants that Algeria said left 23 hostages and 32 militants dead.

The episode has fueled concerns about the growing threat posed by North Africa-based terror groups. It gripped populations and world leaders from Washington to London to Tokyo because citizens from as many as 12 different nationalities were involved and, until late Saturday, little information seeped out...