Kalashnikov assault rifles and ammunition were seized during the operation in the Oued Zhour area of Skikda, the ministry said.
It identified the men only as Habbach, also known as Abou Doujana, and Benaldjia who went by the name of Abderrahman.
Algerian media named the first man as Saddek Habbach, the "emir" or leader in eastern Algeria of Jund al-Khilafa extremist movement which is linked to the jihadist Islamic State group.
Jund al-Khilafa, or Soldiers of the Caliphate, has claimed responsibility for the abduction and murder two years ago in the Kabylie region east of Algiers of French mountain guide Herve Gourdel.
Algeria uses the term of "terrorists" for armed Islamists who have been active in the North African state since a devastating civil war in the 1990s.
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