TIMBUKTU, Mali » When the Islamist militants came to town, Dr. Ibrahim Maiga made a reluctant deal. He would do whatever they asked — treat their wounded, heal their fevers, bandage up without complaint the women they thrashed in the street for failing to cover their heads and faces. In return, they would allow him to keep the hospital running as he wished.

Then, one day in October, the militants called him with some unusual instructions. Put together a team, they said, bring an ambulance and come to a sun-baked public square by sand dunes.

There, before a stunned crowd, the Islamist fighters carried out what they claimed was the only just sentence for theft: cutting off the thief’s hand. As one of the fighters hacked away at the wrist of a terrified, screaming young man strapped to a chair, Maiga, a veteran of grisly emergency room scenes, looked away.

"I was shocked," he said, holding his head in his hands. "But I was powerless. My job is to heal people. What could I do?"

After nearly 10 months of occupation by Islamist fighters, many of them linked with al-Qaida in the Islamic Maghreb, the people of this ancient mud-walled city recounted how they survived the upending of their tranquil lives in a place so remote that its name has become a synonym for the middle of nowhere.

"Our lives were turned upside down," Maiga said. "They had guns, so whatever they asked, we did. It was useless to resist."

It has been only a few days since French and Malian troops marched into Timbuktu after heavy airstrikes chased the militants away, part of a surprisingly rapid campaign to retake northern Mali from the militants who held it captive for months. On Thursday, the French defense minister, Jean-Yves Le Drian, told French radio that the intervention had "succeeded" and reached "a point of change."

But while the Islamist militants have retreated to the desert, there are no illusions that they have ceased to be a threat.

As U.S. officials praised the speed of the French-led operation to recapture northern cities, they also cautioned that a lengthy campaign would be needed to root out the militants from their desert redoubts — and that it was not immediately clear who would carry out the daunting task.

"This is all being done very much on the fly," one U.S. official said of the intervention. "The challenge will be to keep up the pressure when the sense is to declare victory and go home."

Here in Timbuktu, life is certainly a long way from returning to normal. Shops owned by Arab tradesmen have been looted. Some residents have fled, a foretaste of ethnic strife that many fear will roil Mali for years to come. Electricity and running water are available only a few hours a day. The cellphone network remains down.

Many of the residents who left — first to escape the occupation, then to escape the French airstrikes — have no way to return. Always remote, the city remains dangerously isolated: The dusty tracks and rivers leading here wind through forbidding scrubland territory that could still provide refuge for the Islamist fighters who melted away from the cities.

Those who remained told stories of how they survived the long occupation: by hiding away treasured manuscripts and amulets forbidden by the Islamists; burying crates of beer in the desert; standing by as the tombs of saints they venerated were reduced to rubble; silencing their radios to the city’s famous but now forbidden music.

"They tried to take away everything that made Timbuktu Timbuktu," said Mahalmoudou Tandina, a marabout, or Islamic preacher, whose ancestors first settled in Timbuktu from Morocco in the 13th century. "They almost succeeded."

The occupation of Timbuktu, a center of learning for centuries, was the latest in a long historical list of conquests — by Arab nations, by the Songhai and Maasina empires, by France. Once again, powerful global forces were in play in this fabled city: a network of Islamic extremists, the armies of France and West Africa, and to a lesser extent the United States, which has flown in French forces and refueled French warplanes during the campaign.

Through it all, the city’s residents, whose ancestors endured such ravages for the better part of a millennium, have adapted as best they could.

On April 1, the day rebels arrived in this city, Tandina had just returned from the first, predawn prayer of the day. He made bittersweet tea to the murmur of a French radio broadcast. The news was bad: Gao, the largest city in northern Mali, had fallen to Tuareg rebels, the nomadic fighters who had been battling the Malian state for decades.

His hometown was almost certainly their next target. When shots rang out in Independence Square, just behind Tandina’s house, he knew that Timbuktu’s latest conquerors had arrived.

"The barbarians were at our gate," he said with a sigh. "And not for the first time."

Barrel-chested and dressed in a blue tunic, the leader of Ansar Dine, an Islamist group with links to al-Qaida in the Islamic Maghreb, arrived with several truckloads of fighters. The new rebels called the city’s people to a public square and made an announcement.

"They said, ‘We are Muslims. We came here to impose Shariah,"’ Tandina said.

It started with the women. If they showed their faces in the market they would be whipped. The local men grew angry at attacks on their wives, so they organized a march to the headquarters of the Islamic police, who had installed themselves in a bank branch.

The Islamists greeted the protesters by shooting in the air. Many fled, but a small group, including Tandina, insisted that they be heard.

A young, bearded man came out to meet them. Much to Tandina’s surprise, he recognized the Islamic police official. His name was Hassan Ag, and before the fighting began he had been a lab technician at the local hospital.

"When I knew him he was clean-shaven, and he wore ordinary clothes of a bureaucrat," Tandina said.

Now he was dressed in the uniform of the Islamist rebellion: a tunic, loose trousers cut well above the ankle, in imitation of the Prophet Muhammad, and a machine gun slung across his shoulder.

"I told him our women were being harmed," he said.

Ag was unmoved.

"This is Islamic law," he said, according to Tandina. "There is nothing I can do. And the worst is yet to come."

Soon it came. They began destroying tombs of the saints venerated by Timbuktu’s Muslims. Armed with pickaxes and sledgehammers, they reduced to rubble the tomb of Sidi Mahmoud, a saint who, according to legend, protected the city from invaders.

Venerating saints, an ancient practice here, was considered un-Islamic in the austere version of the faith proclaimed by the occupiers.

Tandina said he tried to use his decades of Quranic education to argue with the Islamists, citing verses about respecting the burial places. They would not listen.

Before long, he said, amputations started. Then came the executions. Again he said he tried to intervene, going to the Islamic court with stacks of Islamic law books under his arm.

"Islam was whatever they said it was," he said. "They did not respect the holy book. They respected nothing but their own desires."

For hundreds of years, Timbuktu was one of the world’s most important centers of Islamic learning. The city has dozens of mosques and is famous for the ancient, handwritten manuscripts that city residents have collected for generations, preserving them against waves of invaders and creating a priceless trove of knowledge about the Islamic world and beyond. Many families have long traditions of Islamic learning, passed from father to son.

So many here bristled when the Islamists called the population to lecture them about the proper practice of the religion in which they had been raised.

"What they call Islam is not what we know is Islam," said Dramane Cisse, the 78-year-old imam at one of the city’s biggest and oldest mosques. "They are arrogant bullies who use religion as a veil for their true desires."

But like many Muslims here, he hid away his amulets, prayer beads and other banned religious items. In his mind his faith remained the same.

"I was born in my religion, and I will die in my religion," Cisse said. "I know what I believe, and nothing can change that."

The compromises that Maiga made to keep his hospital going continue to haunt him.

After the young man’s hand was cut off, the Islamists held it aloft and shouted, "God is Great," over and over, he said.

Maiga and his team hustled the young man into the ambulance and rushed him into the operating room to cauterize the wound, giving him powerful painkillers.

"I did what I had to do," he said. "God help us."

© 2013 The New York Times Company