Al-Murabitoun said that the notorious Algerian militant Mokhtar Belmokhtar remained its leader, despite reports that he was killed in a US air strike in Libya in June.
The statement dated July 17 says that Al-Murabitoun is "Qaeda al-Jihad in West Africa" and committed to "directives" by network founder Osama bin Laden to attack the enemy "France and its allies".
Belmokhtar, whose real name is Khaled Abu al-Abbas, allegedly masterminded the 2013 siege of an Algerian gas plant in which 38 hostages, mainly Westerners, were killed.
But Belmokhtar reportedly soon distanced himself from the declaration and vowed backing for IS's jihadist rival Al-Qaeda in what was seen as a sign of a power struggle.
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The one-eyed Belmokhtar, a former chief of Al-Qaeda in the Islamic Maghreb (AQIM) who was nicknamed "The Uncatchable" by an ex-French intelligence chief, was twice condemned to death by Algeria.
He had been reported killed in Mali at least once before the United States, which placed a USD 5 million bounty on his head, targeted him in an air strike in Libya in June.
The group has claimed a series of attacks over the years, including a deadly hostage drama at a Mali hotel earlier this month in which 13 people died including five UN workers.
Belmokhtar founded his Al-Qaeda breakaway group "Signatories in Blood" in 2012, later merging it with MUJAO, one of the jihadist groups that seized northern Mali in early 2012, to form Al-Murabitoun.