French troops have reportedly engaged in street battles against Islamist rebels in the town of Diabaly in central Mali.
The fighting on January 16 came as French troops launched their first ground operation.
France intervened in its former West African colony on January 11 at the request of the Mali government to halt the Islamists' push southward toward the capital, Bamako.
French warplanes have since attacked rebel positions but failed to dislodge them.
French media reports said special forces were fighting alongside the Malian Army against the rebels in Diabaly, some 300 kilometers north of Bamako.
France has some 800 troops on the ground in Mali but their number is expected to rise to 2,500.
A West African regional force is also expected to deploy under a UN Security Council resolution.
The conflict in Mali has raised concerns of an Islamist radicalization across West Africa, with Islamists threatening to take revenge for the French intervention.
In Algeria on January 16, Islamist militants killed two people and took several others hostage in an attack on a gas facility.
The In Amenas gas facility is more than 1,000 kilometers from the border with Mali, but near the border with Libya.
One of those killed in the attack was a French national.
The U.S. State Department has confirmed there are Americans among the group of hostages seized in Algeria.
State Department spokeswoman Victoria Nuland did not say how many U.S. citizens were among the hostages.
An Al-Qaeda-linked group claimed it seized 41 hostages, including seven Americans and other Westerners.
It said the raid, which also left two foreigners dead, was in retaliation for France's intervention in Mali.
Algeria's APS state news agency said the Islamists were holding some 20 people hostage at the gas facility in southern Algeria, which it said was surrounded by Algerian troops.
In comments to French media on January 16, French President Francois Hollande said one of the goals of the Mali intervention was to deter such hostage-takings.
"France cannot accept that its nationals be detained. We are making every contact so that their release can take place in the best possible conditions," Hollande said.
"I also want to say what France's position is," he added. "It is through strong actions, including interventions such as we have staged in Mali, that we will make kidnappers and hostage-takers give up."
With reporting by Reuters, AP, dpa, and AFP