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French forces stationed in the neighboring nation of Ivory Coast were traveling to Mali, said a spokeswoman for the Licorne Force in Abidjan, the Ivorian capital. An adviser to the president of Ivory Coast, who could not be named because he was not authorized to speak publicly, said the troops will join the 550 French forces already in Mali and will head directly to Segou, and beyond to Diabaly.

“They will encircle the rebels,” he said.

However, the French national who was being evacuated from Segou said the email she received from the French Embassy indicated that small groups of rebel fighters were already heading to Segou, a drive that normally takes two to three hours.

The Islamists in northern Mali have long said that if France attacked them, they would strike back at French interests all over Africa and beyond.

On Monday, the commander of one of the al-Qaeda offshoots in northern Mali dared the French to keep attacking them.

“France has opened the gates of hell. … It has fallen into a trap much more dangerous than Iraq, Afghanistan or Somalia,” declared Omar Ould Hamaha, a leader of the Movement for Oneness and Jihad in West Africa, one of the jihadist groups controlling the north, speaking on French radio Europe 1.

Mali’s north, an area the size of France, was occupied by al-Qaeda-linked rebels in April following a coup in the capital. For nearly as long, the international community has debated what to do. In December, the U.N. Security Council adopted a resolution calling for military intervention, but only after an exhaustive list of pre-emptive measures were fulfilled, starting with training the Malian military, a process diplomats said would last until at least September.

All that changed in a matter of hours last week, when French intelligence services spotted two rebel convoys heading south, one on the mostly east-west axis of Douentza to the garrison towns of Mopti and Sevare, and a second heading from a locality north of Diabaly toward Segou.

If either Segou or Mopti were to fall, many feared the Islamists could advance toward the capital.

French President Francois Hollande authorized the airstrikes, which began Friday, initially concentrated in the north. France has sent in Mirage jets stationed in Chad that can carry 550-pound bombs. They are also using Gazelle helicopter gunships and the Rafale jet, based in France.

Britain over the weekend authorized sending several C-17 transport planes to help France bring more troops. The United States is sending drones, as well as communications and logistical support.

“Not a half hour goes by when we don’t see a French plane either taking off or landing,” said Napo Bah, a hotel worker in Sevare, the central town that is a launch pad for the operation. “It’s been a constant since last week, when they authorized the military operation.”

• AP writer Greg Keller in Paris contributed to this article.