Camatte, the kidnapped Frenchman, was snatched from a hotel in the Sahel region of northern Mali on the night of November 25.
The three kidnapped Spaniards were working as volunteers in Mauritania delivering humanitarian aid when they were kidnapped on November 29.
They have been named as Albert Vilalta, 35, Alicia Gamez, 35, and Roque Pascual, 50.
Earlier this year a US-based monitoring group reported that AQIM had claimed responsibility for killing Briton Edwin Dyer, one of a group of six Westerners kidnapped in Niger in January.
The group had said threatened to kill Dyer unless the British government released Abu Qatada, a Muslim cleric, from a UK prison.