Fabius added on Monday that new French airstrikes are targeting fuel depots and bases of Islamist extremists in northern Mali.
He said on French radio station France-Inter that the strikes hit the Kidal region overnight, near the border with Algeria. It's part of a broader effort to cut off supplies to radical fighters who had taken over much of the African country and enforced harsh rules on the population.
The French intervened in Mali on January 11 to stem the advance of the al-Qaeda-linked fighters.
Fabius also said that France wants African forces to assume security responsibility for the historic city of Timbuktu as soon as Tuesday.
Timbuktu has been part of three empires, survived invasions and had countless rulers, and it met its 10-month occupation by extremists with the stoicism of a city that has seen centuries of history.
Timbuktu's 'passive resistance'
The insurgents of Ansar Dine ruled Timbuktu under a brutal form of Islamic law from the time they seized the city in the chaotic aftermath of a March military coup until French-led troops reclaimed it last week.
Unlike Gao, which reacted to the Islamist extremists' rule of northern Mali with violent protests, Timbuktu chose "a form of passive resistance", said Abdoul Salam Ascofare, a 67-year-old retired schoolteacher.
"We had the experience of our grandparents, who had lived through colonisation" by France from 1893, said Ascofare, as he had his white beard trimmed at a salon on a sandy street off the fabled city's main market.
"In one of our libraries we found a letter from some luminaries in Djénne [a town to the south known for its Great Mosque] to the luminaries of Timbuktu advising them not to take up arms against the colonisers, who were stronger than them, and to leave themselves in God's hands," he added.
"In general, the people of Timbuktu are stoic, peaceful, and see everything as an act of God."
Ascofare said he would rather have protested the Islamists' "massive abuses" – destroying the city's ancient saints' tombs, raping women prisoners, cutting off an accused thief's hand, publicly executing an alleged murderer – but the city's "council of sages" ruled there would be no active resistance.
Timbuktu, a caravan town at the edge of the Sahara Desert, rose to fame in the 14th century as a hub of the gold and salt trades and a centre of Islamic learning, known for its priceless ancient manuscripts.
Situated at the start of the northern bend in the Niger River, it has, at different points in its history, been part of the Malian, Songhai and French empires, and survived a devastating Moroccan invasion in 1591.
During the more recent occupation, some people collaborated with the extremists, but they were "people from surrounding villages, illiterates with no work, who got recruited because they didn't know better and were happy to carry a gun", said 38-year-old radio presenter Baba Abdou Toure.
But the people of Timbuktu by and large did nothing to facilitate the Islamist extremists' rule, said Toure, whose station was closed by the extremists.
"The people didn't resist, they lived with the situation. One has to be able to control oneself, remain quiet, pray," said a prominent local religious leader, speaking on condition of anonymity.
'Fear in our stomachs'
"Timbuktu is the only city in the world that has never known anything but Islam, and these people wanted to Islamise us," he added.
Ousmane Alamine Toure, a 72-year-old tailor, remembered the extremists "criss-crossing the city with their heavy weapons".
"We went to sleep at 7pm, went to the market with fear in our stomachs," he said.
But Timbuktu did not fight its occupiers. "We resisted with our patience. That's all." – Sapa-AFP, AP