to be referring to Abdelhamid Abou Zeid, whose death in Mali in February was confirmed by Paris "with certainty" on March 23.
The militant group, which attacked a gas plant in Algeria in January, denied the death in a statement published on Friday on Islamist internet forums, Site, a US-based intelligence monitoring website, reported.
The statement threatened "dark days" for France in north and west Africa.
French forces launched a ground and air campaign in Mali on January 11 against Islamist forces who carved out an enclave in the country's northern mountains, saying they posed an international threat.
Paris said in a statement last month: "The president of the French Republic confirms with certainty the death of Abdelhamid Abou Zeid after an offensive by the French army."
However, AQIM said the French statement was motivated by the government's low poll ratings.
"This is a blatant fallacy by the French President Hollande, who has low popularity and whose party is mired in financial and moral scandals, in order to delude the French and global public about the achievement of a field victory that restores to them their lost confidence, domestically and abroad," it said.
The fate of Abou Zeid and another al Qaeda commander, Mokhtar Belmokhtar, presumed mastermind of the Algerian attack in which more than 60 people were killed, has been murky since Chad, which is fighting alongside France in Mali, reported their deaths in March.
Algerian Ennahar TV, which is well connected with Algeria's security services, said late last month a new commander, Djamel Okacha, had been named to replace Abou Zeid.
An Algerian security source said Okacha, also known as Yahia Abu El Hamam, joined AQIM in northern Mali in 2004.
However, the AQIM statement monitored by SITE said Hamam had not been installed to replace Abou Zeid, but had in fact replaced another leader, Nabil Abu Alqamah, who it said died in a traffic accident last year.
It said he had been installed "eight months ago, and nearly five months before the French invasion of northern Mali", according to the monitoring.