Without naming Abou Zeid, whose death was announced by Chad’s President Idriss Déby on 1 March and confirmed by France on 23 March, Aqim denounced a “blatant error” by French President François Hollande, accusing him of trying to win back popularity by exaggerating the success of the Mali offensive.
And it denied a claim by Algerian television channel Ennahar that Djamel Okacha, alias Yahia Abou el Hamam, had taken over from Abou Zeid.
Hamam has replaced another local leader, Nabil Abou Alqamah, who died in a traffic accident last year, an Aqim statement claimed.
On a visit to Bamako on Friday Fabius said that he had “reassured” the Malian government that France is not planning an "overnight" withdrawal of its forces.
France will propose to the UN and the Malian government that a permanent support force of 1,000 French soldiers “equipped to fight terrorism” stay in Mali, Fabius said.
It is due to pull out most of its troops at the end of April after handing over to a UN-mandated African force of 6,300.
Fabius also called on the Tuareg National Movement for the Liberation of Azawad (MNLA), which switched sides to fight the Islamists alongside the French, to lay down their arms and urged that elections go ahead as planned in July.
"We hope conditions will soon be in place to allow us to organise and complete these elections by July 31. It's a gamble but it is a strong commitment of the Malian government," Prime Minister Diango Cissoko told reporters.