Abou Zeid had been promoted by the emir of AQIM -- and fellow Algerian -- Abdelmalek Droukdel.

CNN: STORY HIGHLIGHTS

The group's overall leader, Abdelmalek Droukdel, appears to have lost patience with Belmoktar's "freelance" kidnapping of Westerners, which are reputed to have netted several million dollars.

CNN: Phone call links Benghazi attack to al Qaeda commander

Abu Zeid was promoted to a deputy leadership position in the Sahara several years ago by AQIM's Emir Abdelmalek Droukdel out of concern that Belmoktar was growing too strong.

CNN: Al Qaeda reported to suffer double blow in Sahara