* French special forces surround city, no rebel resistance
* Retreating insurgents torched manuscript library - mayor
* French try to avoid combat in city to protect treasures
* Islamist rebels pulling back into north desert, mountains (Recasts with details of French operation, manuscript library torched)
French and Malian troops on Monday sealed off Timbuktu, a UNESCO World Heritage site, after fleeing Islamist rebel fighters torched several buildings in the ancient Saharan trading town, including a priceless manuscript library.
Without a shot being fired to stop them, 1,000 French soldiers including paratroopers and 200 Malian troops seized the airport and surrounded the centuries-old Niger River city, looking to block the escape of al Qaeda-allied fighters.
The retaking of Timbuktu followed the swift capture by French and Malian forces at the weekend of Gao, another major northern Malian town which had also been occupied by the alliance of Islamist militant groups since last year.
A two-week intervention by France in its former Sahel colony, at the request of Mali's government but also with wide international backing, has driven the Islamist rebel fighters northwards out of towns into the desert and mountains.
A French military spokesman said the assault forces at Timbuktu were being careful to avoid combat inside the city so as not to damage cultural treasures and mosques and religious shrines in what is considered a seat of Islamic learning.
But Timbuktu's mayor, Ousmane Halle, reported that fleeing Islamist fighters had torched a South African-funded library in the city containing thousands of priceless manuscripts.
"The rebels set fire to the newly-constructed Ahmed Baba Institute built by the South Africans ... this happened four days ago," Halle Ousmane told Reuters by telephone from Bamako. He said he had received the information from his chief of communications who had travelled south from the city a day ago.
Ousmane was not able to immediately say how much the concrete building had been damaged. He added the rebels also torched his office and the home of a member of parliament.
The Ahmed Baba Institute, one of several libraries and collections in the city containing fragile ancient 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 faced no resistance so far at Timbuktu, but they face a tough job of combing through the labyrinth of ancient mosques and monuments and mud-brick homes between alleys to flush out any hiding Islamist fighters.
"We have to be extremely careful. But in general terms, the necessary elements are in place to take control," French army spokesman Lieutenant Thierry Burkhard said in Paris.
Timbuktu member of parliament El Hadj Baba Haïdara told Reuters in Bamako the Islamist rebels had abandoned the city. "They all fled. Before their departure they destroyed some buildings, including private homes," he said.
The United States and European Union are backing the French-led Mali operation as a strike against the threat of radical Islamist jihadists using the West African state's inhospitable Sahara desert as a launch pad for international attacks.
They are helping with intelligence, airlift of troops, refuelling of planes and logistics, but do not plan to send combat troops to Mali.
FRANCE: MALI "BEING LIBERATED"
"Little by little, Mali is being liberated," French Foreign Minister Laurent Fabius told France 2 television.
At Gao, more than 300 km (190 miles) east of Timbuktu, jubilant residents danced to music in the streets on Sunday to celebrate the liberation of this other ancient Niger River town from the sharia-observing rebels.
A third northern town, the Tuareg seat of Kidal, in Mali's rugged and remote northeast, remains in the hands of the Islamist fighters, a loose alliance that groups AQIM with Malian Islamist group Ansar Dine and AQIM splinter MUJWA.
With its cultural treasures, Timbuktu had previously been a destination for adventurous tourists and international scholars.
The world was shocked by its capture on April 1 by Tuareg desert fighters whose separatist rebellion was later hijacked by Islamist radicals who imposed severe sharia law.
Provoking international outrage, the Islamist militants who follow a more conservative Salafist branch of Islam destroyed dozens of ancient shrines in Timbuktu sacred to moderate Sufi Moslems, condemning them as idolatrous and un-Islamic.
They also applied amputations for thieves and stoning of adulterers under sharia, 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 set by the Islamist rebels.
"THREAT OF TERRORISM"
As the French and Malian troops push into northern Mali, African troops from a U.N.-backed continental intervention force expected to number 7,700 are being flown into the country, despite severe delays due to logistical problems.
Outgoing African Union Chairman President Thomas Boni Yayi of Benin at the weekend scolded AU states for their slow response to assist Mali while former colonial power France took the lead in the military operation.
Yayi put the cost of the African intervention force, now revised upwards, at $1 billion and said up to 10 African countries may be required to send troops.
Burkina Faso, Benin, Nigeria, Senegal, Togo, Niger and Chad are providing soldiers. Burundi and other nations have pledged to contribute.
The AU is expected to seek hundreds of millions of dollars in logistical support and funding for the African Mali force at a conference of donors to be held in Addis Ababa on Tuesday.
Yayi also urged other NATO members and Asian countries to follow France's lead and send troops to Mali. "We have to free the Sahel belt from the threat of terrorism," he said.