The French president has said that he will withdraw troops from Mali once the Sahel state has restored sovereignty over its national territory.
A United Nations backed African military force is expected to take over from the French soldiers.
President Hollande said: "We have not yet finished our mission. But we do not foresee staying indefinitely. Once the sovereignty of Mali is restored, once MISMA (the African force) can replace our own troops, we will withdraw,"
France has been involved in a three-week-old military intervention against Islamist rebels in Mali.
The French army has inflicted "heavy losses" on them, but not eliminated the rebels.
Malians chanting "Thank you, France!" mobbed President Francois Hollande as he visited the desert city of Timbuktu, retaken from Islamist rebels, and pledged France's sustained support for Mali to expel jihadists.
Mr Hollande, accompanied by his ministers for defence, foreign affairs and development, was on a one-day trip to the Sahel nation to support French troops who in three weeks have ousted fighters allied with al-Qaeda from Mali's main northern towns.
He met the interim president, Dioncounda Traore, and the two held talks in Timbuktu and later in Bamako, the capital in the south where the French leader also received a rapturous welcome.
Speaking in Timbuktu, President Hollande said the French operation, which has driven the rebels into the mountains of northeast Mali at the cost of only one French serviceman killed so far, would eventually hand over to a larger African military force.
"The combat is not over," he said, flanked by Traore, in a speech praising the French forces.
"We are obliged to support the Malians until they have recovered their entire sovereignty. We'll do it with the Africans," he added separately to reporters.
Mr Traore said: "Together we will hunt the terrorists down to their last hiding place."
The US and the EU are backing the Mali intervention as a counterstrike against the threat of Islamist jihadists using the inhospitable and ungoverned Malian Sahara as a launch pad for international attacks.
They are providing training, logistical and intelligence support, but have ruled out sending their own ground troops.
In Timbuktu, the renowned Saharan trading town and seat of Islamic learning that spent 10 months under rebel occupation.
Mr Hollande visited the Djingarei-ber or Grand Mosque and the Ahmed Baba Institute, a library of ancient manuscripts that was ransacked by the rebels.
President Hollande said it was essential that Timbuktu, a UNESCO World Heritage site, should be properly protected so that it could "shine" as a cultural treasure for the world.