PARIS/DAKAR (Reuters) - A French soldier and more than 20 Islamist rebels were killed during what appeared to be the first clashes in the Adrar des Ifoghas mountain range where militants have taken refuge in northern Mali, French sources said on Tuesday.

Speaking on a visit to Athens, French President Francois Hollande said serious fighting had broken out and was continuing in the remote Adrar des Ifoghas mountains, resulting in several casualties among the rebels and one among the French.

"A legionnaire from the 2nd foreign parachute regiment has died in a clash with Islamists in northern Mali," Hollande told reporters in Athens.

The soldier is the second French casualty since the intervention last month to oust al Qaeda-backed rebels from northern Mali.

The French defense ministry said in a statement that a parachute regiment of 150 soldiers supported by a heavy vehicle patrol and Mirage fighter jets had come under fire on Tuesday morning.

The French raid aimed at disrupting the militants and dismantling their camps, the ministry said.

"The French mission was able to locate terrorist elements in their hideout, to chase them and to kill more than 20 of them," it said.

Around 4,000 French troops, backed by the Malian army and several thousand troops from other African states, have driven the Islamist alliance out of the main cities into the northern mountains.

"We are now in the last phase of the operation," Hollande said.

"It's no longer a question of simply arresting the terrorists, making the territory safe, but to go to the end of the mission and that means arresting the last leaders of these groups that are in the extreme north of Mali."

(Reporting By Vicky Buffery and John Irish; Editing by Michael Roddy)