French-led troops in Mali have entered the historic city of Timbuktu encountering little resistance, French and Malian military sources say. But there are reports of thousands of ancient manuscripts being destroyed, with video footage of the library showing charred books and empty boxes. French President Francois Hollande declared that the joint forces were "winning this battle". They have been pushing north in their offensive against Islamist rebels. They seized Gao, northern Mali's biggest city, on Saturday. Islamists seized the north of the country last year, but have been losing ground since French forces launched an operation earlier this month. Most militants appear to have moved out to desert hideouts, says the BBC's Thomas Fessy in the capital, Bamako. The advance came as African Union (AU) leaders met for a summit in the Ethiopian capital, Addis Ababa, the key issue at which was Mali. The AU decided to contribute $50m (£32m) to the multinational force, in what the BBC's James Copnall says is an attempt to start the ball rolling for what promises to be a costly operation. Library 'emptied' On Monday afternoon, a French military spokesman said troops had moved into Timbuktu. They were met by cheering crowds as they entered, waving French and Malian flags and shouting "Mali, Mali, Mali!". "We are proud of France and proud of Mali. We thank you a thousand times," one resident said. "We are independent again! We were held hostage for 10 months but it seemed like 10 years," AFP news agency quoted resident Hama Cisse as saying. Meanwhile, a Malian army colonel told the agency: "The Malian army and the French army are in complete control of the city of Timbuktu." Soldiers were now patrolling the town to carry out clean-up operations, fearing Islamist elements may still be hiding within the population, the French military said. Reports have emerged that militants had destroyed a library of ancient manuscripts, some dating back to the 13th Century. Sky News correspondent Alex Crawford, who is with the joint forces, showed some charred documents and piles of empty boxes at the library said to have contained the manuscripts, and said vaults beneath the building had been emptied. The library, the Ahmed Baba institute, held about 30,000 manuscripts, and includes documents about centuries of life in the city, Mali and neighbouring countries. 'Strategy of evasion' French army spokesman Col Thierry Burkhard had told the BBC earlier that "substantial airpower" had been used to support about 1,000 French and 200 Malian forces in their offensive against militants in Timbuktu. He said French forces had taken access points to the city during the night. Once Timbuktu is secured, the French-led troops are expected to focus on the last rebel stronghold, Kidal, near the border with Algeria. But reports from the city - which is the home of the head of Ansar Dine, the main militant group in northern Mali - suggest that the group may have lost control there as well. The secular Tuareg rebel group, MNLA, said it had taken charge. AFP quoted a spokesman of an Ansar Dine breakaway faction as saying that it was jointly "ensuring security" with the MNLA. Once Kidal is taken, the first phase of the French operation will be over, our correspondent says. The second phase will be to track down the militants to their desert hideouts, which could prove a much more difficult task, he adds. Mr Fabius warned that the militants had adopted a "strategy of evasion and some of them could return in the north". President Hollande later outlined plans for the operation, saying African troops would take over once French forces had retaken key towns. The French would then return to their bases, and from then on their sole task would be to support and train Malian forces, he added. "Just as we went into action rapidly, we will draw back to the starting points," he said. French officials said they now had 2,900 troops in Mali, backed by 2,700 African forces in Mali and neighbouring Chad. The African contingent is expected to be bolstered to 7,900, including 2,200 troops promised by Chad, AP news agency quotes a Nigerian military official, Col Shehu Usman Abdulkadir, as saying.