The attack on Gao, the largest city in the desert region controlled by the Islamist alliance, marked a decisive intensification on the third day of French air raids, striking at the heart of the vast territory seized by rebels in April.
France is determined to end Islamist domination of north Mali, which many fear could act as a base for attacks on the West and for links with al Qaeda in Yemen, Somalia and North Africa.
France's Defence Minister Jean-Yves Le Drian said French intervention on Friday had prevented the advancing rebels from seizing Bamako. He vowed that air strikes would continue.
"The president is totally determined that we must eradicate these terrorists who threaten the security of Mali, our own country and Europe," he told French television.
In Gao, a dusty town on the banks of the Niger river where Islamists have imposed an extreme form of sharia law, residents said French jets pounded the airport and rebel positions. A huge cloud of black smoke rose from the militants' camp in the city's north, and pick-up trucks ferried dead and wounded to hospital.
"The planes are so fast you can only hear their sound in the sky," resident Soumaila Maiga said by telephone. "We are happy, even though it is frightening. Soon we will be delivered."
Paris said four state-of-the-art Rafale jets flew from France to strike rebel training camps, logistics depots and infrastructure in Gao with the aim of weakening the rebels and preventing them from returning southward.
A spokesman for Ansar Dine, one of the main Islamist factions, said the French had also bombed targets in the towns of Lere and Douentza. Residents said rebel fighters had fled from Douentza aboard pick-up trucks.
France has deployed about 550 soldiers to Mali under "Operation Serval" - named after an African wildcat - split between Bamako and the town of Mopti, 500 km (300 miles) north.
In Bamako, a Reuters cameraman saw more than 100 French troops disembark on Sunday from a military cargo plane at the international airport, on the outskirts of the capital.
The city itself was calm, with the sun streaking through the dust enveloping the city as the seasonal Harmattan wind blew from the Sahara. Some cars drove around with French flags draped from the windows to celebrate Paris's intervention.
AFRICAN TROOPS EXPECTED
More than two decades of peaceful elections had earned Mali a reputation as a bulwark of democracy, but that image unravelled in a matter of weeks after a military coup in March which left a power vacuum for the Islamist rebellion.
French President Francois Hollande's intervention in Mali has won plaudits from leaders in Europe, Africa and the United States but it is not without risks.
It raised the threat level for eight French hostages held by al Qaeda allies in the Sahara and for the 30,000 French expatriates living in neighbouring, mostly Muslim states.
Concerned about reprisals, France has tightened security at public buildings and on public transport. It advised its 6,000 citizens to leave Mali as spokesmen for Ansar Dine and al Qaeda's north Africa wing AQIM promised to exact revenge.
In its first casualty of the campaign, Paris said a French pilot was killed on Friday when rebels shot down his helicopter.
Hours earlier, a French intelligence officer held hostage in Somalia by al Shabaab extremists linked to al Qaeda was killed in a failed commando raid to free him.
President Hollande says France's aim is simply to support a mission by West African bloc ECOWAS to retake the north, as mandated by a U.N. Security Council resolution in December.
With Paris pressing West African nations to send their troops quickly, Ivory Coast President Alassane Ouattara, who holds the rotating ECOWAS chairmanship, kick-started the operation to deploy 3,300 African soldiers.
Ouattara, installed in power with French military backing in 2011, convened a summit of the 15-nation bloc for Saturday in Ivory Coast to discuss the mission.
"The troops will start arriving in Bamako today and tomorrow," said Ali Coulibaly, Ivory Coast's African Integration Minister. "They will be convoyed to the front."
The United States is considering sending a small number of unarmed surveillance drones to Mali as well as providing logistics support, a U.S. official told Reuters. Britain and Canada have also promised logistical support.
Former French colonies Senegal, Niger and Burkina Faso have all pledged to deploy 500 troops within days. In contrast, regional powerhouse Nigeria, due to lead the ECOWAS force, has suggested it would take time to train and equip the troops.
France, however, appeared to have assumed control of the operation on the ground. Its airstrikes allowed Malian troops to drive the Islamists out of the strategic town of Konna, which they had briefly seized this week in their southward advance.
Analysts expressed doubt, however, that African nations would be able to mount a swift operation to retake north Mali - a harsh, sparsely populated terrain the size of France - as neither the equipment nor ground troops were prepared.
"My first impression is that this is an emergency patch in a very dangerous situation," said Gregory Mann, associate professor of history at Columbia University, who specialises in francophone Africa and Mali in particular.
While France and its allies may be able to drive rebel fighters from large towns, they could struggle to prise them from mountain redoubts in the region of Kidal, 300 km (200 miles) northeast of Gao, where April's uprising began.
Calm returned to Konna on Sunday after three nights of combat as the Malian army mopped up any rebel fighters. A senior Malian army official said more than 100 rebels had been killed.
"Soldiers are patrolling the streets and have encircled the town," one resident, Madame Coulibaly, told Reuters by phone. "They are searching houses for arms or hidden Islamists."
Human Rights Watch said at least 11 civilians, including three children, had been killed in the fighting.
A spokesman for Doctors Without Borders in neighbouring Mauritania said about 200 Malian refugees had fled across the border to a camp at Fassala and more were on their way.
In Bamako, civilians tried to contribute to the war effort.
"We are very proud and relieved that the army was able to drive the jihadists out of Konna. We hope it will not end there, that is why I'm helping in my own way," said civil servant Ibrahima Kalossi, 32, one of over 40 people who queued to donate blood for wounded soldiers.