Around 15 Islamist militants were killed by French and Chadian troops in fighting overnight in northern Mali's Ametetai valley, French Defence Minister Jean-Yves Le Drian said on Tuesday.
He said some 1,600 French and Chadian troops operating in the area continued to search for Islamist rebels.
France is still not in a position, however, to confirm reports that the military operation has killed two key al Qaeda commanders, Abdelhamid Abou Zeid and Mokhtar Belmokhtar, Le Drian told BFM TV.
Shown a photograph published in French media of a partly shrouded corpse said to be Belmokhtar's, Le Drian said it would be good news if it was the jihadist leader but that he was not convinced by the image.
"Our forces fought terrorist groups last night, still in the same area, the Ametetai valley region, where there is a strong concentration of them. Around 15 militants were killed," Le Drian said.
"It's not over yet as after the Ametetai valley there are other valleys ... Given the ferocity of the fighting over the past fortnight, we can see there is a hideout there."
Three French soldiers and dozens of Islamists have been killed in a seven-week campaign that has driven al Qaeda-linked fighters who took over northern Mali last April back into mountain and desert redoubts, where they are being hunted by hundreds of French, Chadian and Malian troops.
Al Qaeda in the Islamic Maghreb (AQIM) has pledged to avenge the French assault, which Paris says it launched due to fears that its former colony could become a launch pad for wider Islamist attacks.
Asked about the risks of the fighting to a French family taken hostage in Cameroon last month by Islamist militants and taken into Nigeria, Le Drian said France had information on the whereabouts of the three adults and four children, and everything indicated they were still alive.
"I think if the hostages had been killed, their captors would have let it be known," he said. "We are using all the means we can to get them freed.