"The special forces are currently in Diabaly, in close-quarter combat with the Islamists. The Malian army is also in place," the Malian security source told news agency AFP on condition of anonymity.
Earlier, France’s army chief confirmed French troops have begun a ground offensive in Mali.
"The ground operation began several hours ago," Admiral Edouard Guillaud told Europe 1 radio on Wednesday morning.
French armoured units and Malian government forces set off towards the north from the capital Bamako, supporting airstrikes that began last week.
French Defence Minister Jean-Yves Le Drian confirmed that the troops, whose number is set to triple from 800 at present to 2,500 men, faced a long and tough battle against determined fighters whose number he estimated at up to 1,300.
"It's a little more difficult in the west, where we have the toughest, most fanatical and best-organised groups. It's under way there but it's difficult," he said.
A first contingent of 190 Nigerian troops was also due to arrive in Bamako on Wednesday as part of a regional force of over 3,000 soldiers from Benin, Ghana, Niger, Senegal, Burkina Faso and Togo to support the French and Malian troops.
In addition, Germany announced today it would send two military transport planes to support the mission, with the planes mainly used to move African troops.
Belgium has offered two C-130 transport planes and two helicopters to back up
France's offensive, while Britain and Canada have offered troop transporters.
On the ground, a military source said the Islamists were some 80 kilometres north of Markala, putting them around 350 kilometres away from Bamako.
A convoy of armoured vehicles was also reported by a local government official to be heading to the town of Diabaly, which Al Qaeda-linked groups seized earlier this week.
The United Nations humanitarian agency said on Tuesday 144,500 refugees have fled the unrest to neighbouring Mauritania, Niger, Burkina Faso and Algeria, while another 230,000 were internally displaced.