"The preliminary investigation has identified certain members of the terrorist group that carried out this crime," Tayeb Louh said on state television.
Gourdel was seized on September 21 by Jund al-Khilifa, or "Soldiers of the Caliphate," a group linked to the Islamic State jihadists, while trekking in a national park in eastern Algeria.
The 55-year-old mountain guide was beheaded, in a video posted online last Wednesday, after France rejected the kidnappers' ultimatum to halt anti-IS air raids in Iraq.