Mali's defence ministry said on Saturday the armed forces had killed about 20 northern separatist rebels and taken a dozen more prisoner during two days of clashes in the Timbuktu region.
Tuareg-led MNLA rebels made no immediate comment.
Sporadic heavy weapons fire was heard also on Saturday near the northern town of Kidal, northeast of Timbuktu, which the rebellion says it is in the process of attacking.
Veteran Tuareg insurgents and men returning from Libya's war last year are fighting to create an independent state in north Mali. They have gained ground in a three-pronged advance, scattering thousands across Mali's north and beyond its borders.
Mali's defence ministry said that the rebels had been killed during two days of operations in Timbuktu, one of three regions targeted by the MNLA. There were no losses on the government side, according to the statement.
The government gave no further details on the clashes but a Malian military source and a local journalist said most of the rebels were killed when air force helicopters attacked rebel positions near the town of Niafunke on Saturday.
Hama Ag Sid'Ahmed, a Europe-based spokesman for the rebels, confirmed that military operations were taking place near Niafunke but said it was too early to give a toll.
Residents in Kidal, a town in north Mali, said that they had heard sporadic heavy weapons fire overnight and through Saturday morning. Sid'Ahmed said the firing came from an MNLA attack on Kidal, which would be the most significant target yet since clashes erupted in mid-January.
We will take the two military camps and occupy the town, he said.
However military sources in Kidal and the capital, Bamako, said the sound of gunfire came from army units warding off a rebel attack following rumours that the MNLA were due to strike on Saturday.
Civilians, fearing an attack, have been fleeing Kidal by bus in recent days. Some Tuaregs say many of their community have also fled Bamako, in the south, fearing reprisals after violent demonstrations this week.
About 3,500 people had crossed westwards into Mauritania, said a Mauritanian official, who asked not to be named.
The International Committee for the Red Cross said on Friday that nearly 10,000 people had fled into Niger after fighting between the army and armed groups in the area around Menaka and Anderamboucane, in the northeast of Mali.
One refugee in Niger, Aminatou Sango, said everyone tried to flee. I left my very old mother and one of my daughters as they could not walk. I am here alone.
The rebels say they are fighting to secure the independence of Azawad - Mali's three northern regions, Kidal, Timbuktu and Gau. The government accuses the rebels of atrocities and collaborating with al Qaeda, a charge the MNLA rejects.
The ICRC said that some refugees were being looked after by local families while others had set up makeshift camps.
The aid group said the refugees were crossing into a desert region of Niger that is expected to be hit hard by a food crisis this year.
(Additional reporting by Nathalie Prevost in Sinagodor and David Lewis; Writing by David Lewis; Editing by Louise Ireland)