Flying at low altitude, the two helicopters crashed into each other.

“It was very dark,” the French defense minister, Florence Parly, said at an afternoon news conference. “It was moonless.” The soldiers on the ground had already engaged the jihadists, Ms. Parly said, and they had asked for air support.

She said the “combat and operational conditions are extremely demanding.”

There were no survivors among the French soldiers, officials said. Those killed were commandos and “elite soldiers” of the ground army, Ms. Parly said. The crash occurred in what is currently the most sensitive and Islamist-plagued zone, Mali’s southeast, near the lawless border with Niger. The authority of the government in these border zones, far from the capital, is minimal.

“These 13 heroes had just one goal: to protect us,” President Emmanuel Macron wrote on Twitter on Tuesday.

French forces in the region are seen as essential support to weak local armies that have been struggling to contain the threat from Islamic State-affiliated extremists.

Attacks are frequent and the armies in Mali and in Burkina Faso appear powerless either to head them off or to limit their own losses. Just a week ago, 24 Malian soldiers were killed in the same region when their patrol was attacked. The Malians said 17 jihadists had also been killed.