French Foreign Minister Laurent Fabius has said that its military operation in Mali would be not be a long one Al Jazeera reported.
"Stopping the terrorists - it's done," Fabius said on Sunday. "Today we started taking care of the terrorists' rear bases."
Asked how long France would take a leading role in the conflict, he replied "it is a question of weeks".
French warplanes have struck further north in Mali, pounding Islamist strongholds and forcing the insurgents to flee, as preparations for the African intervention force took shape in the capital.
In the third day of the French intervention on Sunday Rafale fighter planes struck bases used by al-Qaeda-linked fighters in Gao, the main city in northern Mali.
Their warplanes also attacked rebel stockpiles of munitions and fuel further north at Afhabo, 50 km from Kidal, a regional security source said. The area is a stronghold of Ansar Dine (Defenders of Faith).
And they hit a base further east at Lere, near the border with Mauritania, according to witnesses and a statement from Doctors Without Borders (MSF).
Algeria on Sunday granted France permission to fly through its airspace to reach its targets, Fabius added. Until now, Algiers has been hostile to any foreign intervention in Mali.
'Good job'
France launched the operation alongside the Malian army on Friday to counter a push south by the insurgents who had threatened to advance on the capital Bamako.
Residents in Gao, which has been under the control of the Movement for Oneness and Jihad in West Africa (MUJAO), said the French airstrikes had levelled the Islamists' position and forced them to flee.
"We can see smoke billowing from the base. There isn't a single Islamist left in town. They have all fled," a teacher said, speaking on condition of anonymity.
"The French have done a good job. Nearly all the Islamists have fled Gao," said one local official, who also asked not to be named. "Those who are still there are hidden in houses and are waiting nightfall to flee."
"What we need now is for the (Malian) army to come here so that the Islamists can't come back," a young student said.
Residents of Timbuktu, which has seen some of the worst Islamist abuses over the past 10 months, said they were eager for French jets to arrive.
"Everyone agrees," said one resident, even if there was a risk that civilians might be killed in such an action. Already, he said, there was growing panic among the Islamists there.
In France itself, authorities were on high alert over fears of a backlash on home soil by Islamist extremists.
French President Francois Hollande will hold a cabinet meeting devoted to the Mali crisis on Monday morning, his office announced.
And at the request of Paris, the UN Security Council will meet later on Monday to discuss the conflict, a spokesman for France's UN mission said.
Aides to Hollande described the militants as better trained and armed than expected.
"What has struck us markedly is how modern their equipment is and their ability to use it," one said, referring to the rebels' hit on a French helicopter, which fatally wounded its pilot, France's only confirmed loss.