Security was tightened in Gao following the two suicide bombings
Heavy gunfire has been heard on the streets of Gao in northern Mali.
A BBC correspondent there says it is coming from the direction of a police station. Some reports said Malian troops were fighting Islamist rebels.
It comes a day after a suicide bomber blew himself up near a checkpoint at a northern entrance to the town - the second such attack in two days.
Gao was retaken just over two weeks ago by French and Malian forces, who supposedly drove out the Islamists.
Security had reportedly been tightened in the wake of the suicide bombings, with military patrols stepped up and checkpoints put in place.
It is not yet known which group is involved in Sunday's clashes.
However, the Movement for Oneness and Jihad in West Africa (Mujao) has said it was behind the suicide attack on Friday, which injured a soldier at the same checkpoint hit on Saturday, and threatened more.
"We are dedicating ourselves to carrying out more attacks against France and its allies. We ask the local population to stay far away from military zones and avoid explosions," spokesman Abou Walid Sahraoui said.
Residents of Gao and a correspondent for the AFP news agency said the gunfire in the town centre was the result of a battle between Islamist militants and Malian forces deployed near the central police station.
There was no immediate comment from the Malian and French militaries.