Al-Qaeda gets the most attention, but local groups and ethnic fighters are part of a complicated mix of instability.
French and Malian troops have entered the key central Malian towns of Diabaly and Doutenza, both of which have been in the hands of al-Qaeda-linked rebels for weeks.
A convoy of about 30 armoured vehicles carrying about 200 French and Malian soldiers moved into the town on Monday at about 09:00 GMT, without meeting resistance.
Diabaly, 350km north of the capital Bamako, had harboured the main cluster of rebels south of the frontline towns of Mopti and Sevare until French air attacks forced them to flee or attempt to blend in with locals, residents said.
A colonel in the Malian army had said earlier that a “fringe of the Diabaly population adheres to the jihadists’ theories and we must be very careful in the coming hours”.
French television footage from Diabaly has shown charred pick-up trucks abandoned by rebels amid mud brick homes.
One resident said the rebels had fled the town which was abandoned by many of its residents, and those remaining lacked food and other essentials.
“We are truly really grateful to the French who came in the nick of time,” said Gaoussou Kone, 34, the head of a local youth association. “Without the French, not only would there not be a Diabaly, there would soon no longer be a Mali.”
‘Total reconquest of Mali’
Malian officials also said that fighters had retreated from Doutenza, where French and Malian forces arrived on Monday morning. A local town adviser said there was no sign of the rebels when the troops arrived.
Paris said the aim of the 11-day old military offensive was total victory. “The goal is the total reconquest of Mali,” Jean-Yves Le Drian, French defence minister, said in televised remarks. “We will not leave any pockets” of resistance.
France began its military offensive in Mali on January 11, and has said that African nations must take the lead though it could be some weeks before they are ready to do so. Britain said on Monday that it would consider giving more help to French forces, but would not take a combat role in the conflict.
Rebels in Mali were reported Sunday to be abandoning some of their positions and converging on the mountainous region of Kidal, their northernmost bastion, 1,500km from Bamako and near the border with Algeria.
Kidal was the first town seized by an amalgam of fighters, some linked to al-Qaeda, and Tuareg separatist groups that started the rebellion in March last year.
Al Jazeera’s Jacky Rowland said there are reports of further Tuareg defections from the rebels as they feel their rebellion has been “hijacked” by the al-Qaeda affilated groups.
“The Tuareg have sensed which way the wind is blowing and they’re afraid of ending up on the wrong side as and when this conflict is resolved,” she said.
Meanwhile, the planned deployment of nearly 6,000 African soldiers continued slowly into Bamako, hampered by cash and logistical constraints. Only 150 African troops had arrived by Sunday.
Senegal, Benin and six other West African nations are contributing to the African mission which is expected to take over the baton from France, and Chad has also pledged 2,000 soldiers.
Desire Kadre Ouedraogo, head of the Commission of regional west African bloc ECOWAS, estimated the cost of an African offensive against the armed Islamist groups at about $500m.
The European Union has pledged 50m euros to the International Support Mission for Mali.