Admiral Edouard Guillaud, the French army's chief of staff, has said he is "extremely cautious" about the reported killing of Mokhtar Belmokhtar, a rebel commander in Mali.
Chad's military said on Sunday that its soldiers had killed Belmokhtar, the leader of a bloody mass hostage-taking at an Algerian gas plant earlier this year.
Guillaud also said Abdelhamid Abou Zeid, a senior leader of al-Qaeda in the Maghreb (AQIM), had "likely" been killed in Mali as also reported by Chadian forces.
"It is likely, but it is only likely," Guillaud said on Monday when asked on France's Europe 1 radio about the reported death, adding that French authorities cannot "have any certainty right now because we have not recovered the body".
The admiral said French forces in Mali had uncovered an "industrial terrorist organisation" in the northeast, where French and Chadian troops are hunting down rebels driven from northern Mali's main cities by a lightning French-led offensive launched in mid-January.
French forces have so far found more than 50 weapons caches, a dozen workshops and 20 improvised explosive devices, he said.
Guillaud also said the French army "has no information" about where French hostages being held in the Sahel region may currently be located. He said it was "possible" they had been moved.
Guillaud said the military operation was dealing a fatal blow to AQIM.
"We are breaking the back of al-Qaeda in the Islamic Maghreb, that was the goal set by the president," he said.
He said the French military was not surprised that fighting had intensified in recent days as rebels have been cornered in mountain hideouts.
"We knew this would be the hardest part of this campaign," Guillaud said.
France said on Sunday a third French soldier had been killed during fierce fighting with rebels in the north of the country.
France's defence ministry said 26-year-old Corporal Cedric Charenton was shot dead on Saturday during an assault on hideout in the desolate Adrar des Ifoghas mountains near Algeria, the third French soldier killed in the campaign.