* French forces surround ancient city, no rebel resistance
* Retreating insurgents burn down manuscript library -mayor
* Tuareg pro-autonomy rebels say they hold Kidal in north
* Islamist rebels pulling back into northern desert, mountains
* AU official sees "clean-up" operation for African troops (Adds detail)
By Adama Diarra
GAO, Mali, Jan 28 (Reuters) - French and Malian troops retook control of Timbuktu, a UNESCO World Heritage site, on Monday after Islamist rebel occupiers fled the ancient Sahara trading town and torched several buildings, including a library holding priceless manuscripts.
The United States and the European Union are backing a French-led intervention in Mali against al Qaeda-allied militants they fear could use the West African state's desert north as a springboard for international attacks.
The recovery of Timbuktu followed the swift capture by French and Malian forces at the weekend of Gao, another major town in Mali's north that had been occupied by the alliance of jihadist groups since last year.
The two-week-old mission by France in its former Sahel colony, at the request of Mali's government, has driven the Islamist rebels northwards out of towns into the desert and mountains.
Without a shot being fired, 1,000 French soldiers and paratroopers and 200 Malian troops seized Timbuktu airport and surrounded the town on the banks of the Niger River, looking to block the escape of insurgents.
In both Timbuktu and Gao, cheering crowds turned out to welcome the French and Malian troops.
A third town in Mali's vast desert north, Kidal, had remained in Islamist militant hands. But Malian Tuareg MNLA rebels, who are seeking autonomy for their northern region, said on Monday they had taken charge in Kidal after Islamist fighters abandoned it.
A diplomat in Bamako confirmed the MNLA takeover of Kidal.
A French military spokesman said the assault forces at Timbuktu were avoiding any fighting inside the city to protect the cultural treasures, mosques and religious shrines in what is considered a seat of Islamic learning.
But Timbuktu Mayor Ousmane Halle told Reuters departing Islamist gunmen had four days earlier set fire to the town's new Ahmed Baba Institute, which contained thousands of manuscripts.
UNESCO spokesman Roni Amelan said the Paris-based U.N. cultural agency was "horrified" by the news of the fire, but was awaiting a full assessment of the damage.
Ali Baba, a worker at the Ahmed Baba Institute, told Sky News in Timbuktu more than 3,000 manuscripts had been destroyed. "They are bandits. They have burned some manuscripts and also stole a lot of manuscripts which they took with them," he said.
Marie Rodet, an African history lecturer at Britain's School of Oriental and African Studies, said Timbuktu held one of the greatest libraries of Islamic manuscripts in the world.
"It's pure retaliation. They (the Islamist militant rebels) knew they were losing the battle and they hit where it really hurts," Rodet told Reuters. "These people are not interested in any intellectual debate. They are anti-intellectual."
ISLAMISTS "ALL FLED"
The Ahmed Baba Institute, one of several libraries and collections in Timbuktu containing fragile documents dating back to the 13th century, is named after a Timbuktu-born contemporary of William Shakespeare and houses more than 20,000 scholarly manuscripts. Some were stored in underground vaults.
The French and Malians have encountered no resistance so far in Timbuktu. But they will now have to comb through a labyrinth of ancient mosques, monuments, mud-brick homes and narrow alleyways to flush out any hiding fighters.
The Islamist forces comprise a loose alliance that groups Al Qaeda in the Islamic Maghreb (AQIM) with Malian Islamist group Ansar Dine and AQIM splinter MUJWA.
They have retreated in the face of relentless French air strikes and superior firepower and are believed to be sheltering in the rugged Adrar des Ifoghas mountain range, north of Kidal.
The MNLA Tuareg rebels who say they now hold Kidal have offered to help the French-led offensive against the al Qaeda-affiliated Islamists. It was not clear, however, whether the French and Malians would steer their offensive further towards Kidal, or hold negotiations with the MNLA.
FRANCE: MALI "BEING LIBERATED"
The world was shocked by Timbuktu's capture in April by Tuareg fighters, whose separatist rebellion was later hijacked by Islamist radicals who imposed severe sharia (Islamic law).
Provoking international outrage, the Muslim militants - who follow a more radical Salafist brand of Islam - destroyed dozens of ancient shrines in Timbuktu sacred to Sufi Muslims, condemning them as idolatrous and un-Islamic.
They also imposed a strict form of Islamic law, or sharia, authorising the stoning of adulterers and amputations for thieves, while forcing women to go veiled.
On Sunday, many women among the thousands of Gao residents who came out to celebrate the rebels' expulsion made a point of going unveiled. Other residents smoked cigarettes and played music to flout the bans previously imposed by the rebels.
Hundreds of troops from Niger and Chad have been brought to Gao to help secure the town.
"Little by little, Mali is being liberated," French Foreign Minister Laurent Fabius told France 2 television.
Speaking at a news conference in Paris, French President Francois Hollande said French troops would take a step back once the job of retaking key towns was complete, and Malian and other African troops would take over the task of hunting the rebels.
"They are the ones who will go into the northern part, which we know is the most difficult because that's where the terrorists are hiding," Hollande said.
As the French and Malian troops thrust into northern Mali, African troops for a U.N.-backed continental intervention force for Mali, expected to number 7,700, are being flown into the country, despite severe delays and logistical problems.
Outgoing African Union Chairman President Thomas Boni Yayi of Benin scolded AU states at a weekend summit in Addis Ababa for their slow response to assist Mali while former colonial power France took the lead in the military operation.
Burkina Faso, Benin, Nigeria, Senegal, Togo, Niger and Chad are providing soldiers for the AFISMA force. Burundi and other nations have pledged to contribute.
AU Peace and Security Commissioner Ramtane Lamamra said these regional troops could play a useful "clean-up" role once the main military operations against the Islamist rebels end.
Speaking in Addis Ababa on Monday, U.N. Secretary-General Ban Ki-moon said the U.N. was "actively considering" helping the troop-contributing African countries with logistical support. (Additional reporting by Richard Valdmanis in Sevare, Mali, Bate Felix and David Lewis in Dakar, Maria Golovina in London, Alexandria Sage, Vicky Buffery and Emmanuel Jarry in Paris, Tiemoko Diallo in Bamako, Abdoulaye Massalatchi in Niamey, Richard Lough and Aaron Masho in Addis Ababa; Writing by Pascal Fletcher; Editing by Andrew Heavens)