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Thierry Burkhard, spokesman for the French army in Paris, said on Sunday the overnight raids targeted logistics bases and training camps used by the al Qaeda-linked rebels to the north of the desert town of Kidal.
"These were important air strikes," Burkhard told Reuters.
He said the bombing raids took place around the settlement of Tessalit, close to the Algerian border, one of the main gateways into the Adrar des Ifoghas mountains where the rebels are believed to be hiding after fleeing major towns.
Malian military sources said French and Chadian troops had clashed with members of the Ansar Dine militant group in the region around Kidal on Saturday.
French attack helicopters and transport planes carrying special forces left the city of Gao to reinforce the French and Chadian contingent stationed at the airport in Kidal.
The town of Kidal itself is under the control of the pro-autonomy MNLA Tuareg rebel group, which occupied it after Ansar Dine fighters fled six days ago.
France has deployed 3,500 ground troops, fighter jets and armoured vehicles in the three-week-old Operation Serval (Wildcat) which has broken the Islamists' 10-month-old grip on the towns of northern Mali, where they had violently imposed sharia law.
Cheering, grateful Malians mobbed Hollande during his one-day visit to Mali on Saturday, when he congratulated French forces and pledged that they would finish the job of restoring government control in the Sahel region state.
"There are risks of terrorism, so we have not finished our mission yet," Hollande told a news conference at the French ambassador's residence in the capital Bamako.
He added France would withdraw its troops from Mali once the West African country had restored sovereignty over all its national territory and a U.N.-backed African military force, which is being deployed, could take over from the French.
"We do not foresee staying indefinitely," he said, but he spelled out no specific timeframe for the French mission.
The United States and the European Union are backing the Mali intervention to defuse the threat of Islamist jihadists using the lawless Malian Sahara as a launchpad for international attacks.
They are providing training, logistical and intelligence support, but have ruled out sending their own ground troops.
Malian Foreign Minister Tieman Coulibaly welcomed the success of France's military operation but urged the former colonial power not to consider scaling back its mission.
"Faced with hardened fighters whose arsenals must be destroyed, we want this mission to continue. Especially as the aerial dimension is very important," he told France's Journal Du Dimanche newspaper.
Paris has pressed Bamako to open negotiations with the MNLA, whose uprising last year triggered a military coup in Bamako in March, as a step toward political reunification of north and south Mali.
The MNLA seized north Mali in April, before being pushed aside by a better-armed Islamist alliance composed of al Qaeda's north African wing AQIM, splinter group MUJWA and Ansar Dine.
Coulibaly played down the possibility of direct talks with the MNLA but said it was clear that there needed to be a greater devolution of power from the mainly black African south to northern Mali, an underdeveloped region home to many lighter-skinned Tuaregs and Arabs.
He called for northern armed groups to lay down their weapons before peace negotiations could begin and said Mali would press ahead with national elections scheduled for July 31.
- Elena Berton and Tiemoko Diallo