A French colonel, exhausted from fighting and who wished not to be named, told CNN that foreign fighters -- including some who are Algerian -- have been pushed out of the area.
Sogoba told CNN the fight against the rebels was very hard, but he is focused on "preserving the national integrity" of Mali.
The humanitarian crisis in Mali is stark, according to the Norwegian Internal Displacement Monitoring Centre.
"They cannot stay where they are due to the grave insecurity caused by the conflict," said Sebastian Albuja, the center's head of the Africa and Americas Department. "Yet the meager resources and the diminished coping abilities of the government and humanitarian actors means that they are faced with limited options."
Because Algeria has closed its borders, people in the north are increasingly heading to the desert, where they will face harsh conditions and real struggles over food and water with limited humanitarian assistance, the group said.
Many are fleeing on foot because they can't afford boats or buses, Albuja said, and even if they do make it, they get there only to find the roads blocked.
The group is especially concerned about women, children and the injured, who they've heard are too afraid to go to hospitals, believing hospitals will be bombed. The Norwegian center is very concerned about victims of rape as a weapon of war, he said.
French involvement began the day after militants said January 10 that they had seized the city of Konna, east of Diabaly in central Mali.
Paris-Match interviews Belmoktar
On Monday, the website of the French magazine Paris-Match published an interview with the spokesman for Moktar Belmoktar, the veteran jihadist behind the Algeria attack, who said the attack was "a 90% success because we managed to reach a strategic site protected by 800 soldiers with only 40 men."