The Taliban admitted Saturday that it lost the strategically vital city of Mazar-e-Sharif to the Northern Alliance.

With the assistance of U.S. bombing, opposition troops said they were hunting down Taliban fighters as they withdrew from the city, which had already changed hands several times in the late 1990s and was the site of massacres.

"This morning the city is quiet," said Karim Khalili, spokesman for the Shiite Muslim faction of the opposition. "There is no fighting. All the Taliban are gone."

Anti-Taliban forces also quickly claimed three northern provincial capitals — Shibarghan in Jozjan province; Aybak in Samangan province; and Maimana in Faryab province — after the capture of Mazar-e-Sharif, according to Mohammed Mohaqik, an opposition commander.

Taliban officials had no comment on the opposition claims, and no foreign reporters were in the area. But adding Aybak to the opposition's control would close off the primary escape route for Taliban soldiers withdrawing from Mazar-e-Sharif to Kabul.

"Hundreds of Arab and Pakistani volunteers fighting with the Islamic militia were hiding in a school six miles west of Mazar-e-Sharif, anti-Taliban officials said.

"Our soldiers are trying to take them alive," said Saeed Zaher Wasik, a spokesman for the Shiite Muslim faction of the opposition Northern Alliance. The report could not be independently confirmed.

President Bush and Pakistani President Pervez Musharraf urged northern alliance forces not to take the capital city of Kabul in an effort to ensure that any post-Taliban government shared power among all the tribes in Afghanistan.

While Bush encouraged the alliance to move southward, he also said that "any power arrangement must be shared with the different tribes within Afghanistan, and a key signal of that will be how the city of Kabul is treated."

Afghanistan contains numerous ethnic tribes. The Northern alliance includes Uzbeks, Tajiks and others; the Pashtun are predominantly located in the south.

Musharraf said if the alliance takes Kabul, "we'll see the same kind of atrocities being perpetuated against the people there" as after the Soviet Union left Afghanistan more than a decade ago. Earlier, in comments to The Washington Post, Musharraf echoed Secretary of State Colin Powell's earlier statements that Kabul should be maintained as a demilitarized city.

Seizing Mazar-e-Sharif marks the most crucial military success since Bush initiated airstrikes Oct. 7 to force the Taliban to hand over Usama bin Laden, chief suspect in the Sept. 11 terrorist attacks on the United States.

Mazar-e-Sharif is vital for military strategy – it gives U.S.-led forces their first major staging ground in Afghanistan for the campaign against the Taliban.

Claiming this city also opens up a land bridge to neighboring Uzbekistan that will allow a wealth of weapons and supplies to be moved to the opposition.

Continuous bombing by U.S. warplanes had forced Taliban fighters to retreat from the city Friday with their weapons and equipment, the Taliban's Bakhtar News Agency said.

"For seven days continuously, they have been bombing Taliban positions. They used very large bombs," said Bakhtar chief Abdul Henan Hemat.

Capitalizing on their victory, anti-Taliban troops also took control of Hairatan on the Afghan border with Uzbekistan, said Mohammed Abil, a spokesman for Burhanuddin Rabbani, the titular head of the Afghan opposition.

The front line had shifted to a road junction, about 12 miles east of Mazar-e-Sharif, which leads to Pul-e-Kumri in the southeast, Abil said. He also said opposition soldiers had taken Taliban mountaintop positions overlooking Taloqan, the capital of northeast Takhar province.

The reports could not be independently confirmed.

Alliance fighters were warmly greeted by Mazar-e-Sharif residents when they entered the city, said Mohammed Hasham Saad, the top opposition official in Uzbekistan. The majority of the city's population, along with the majority of Northern Alliance soldiers, is ethnic Tajiks and Uzbeks.

"They helped our forces move inside of the city and gave them food and information," Saad said. Some civilians pointed out Taliban positions to alliance fighters, he said.

He said Radio Mazar-e-Sharif had begun broadcasting and that one of the first messages to the people was from Rabbani, the former Afghan president who was ousted by the Taliban in 1996.

In Dushanbe, Tajikistan, the Northern Alliance's foreign minister, Abdullah, said the Taliban had left 20 tanks and many heavy weapons behind. At least 20 Taliban fighters were killed and hundreds were taken prisoner, he said.

Meanwhile, American B-52 bombers and other warplanes attacked at the front line north of Kabul on Saturday, and huge clouds of smoke billowed up from Taliban positions.

Anti-Taliban troops at the front were cheered by the news of the fall of Mazar-e-Sharif, Villagers crowded around transistor radios to hear the latest news.

"This is the beginning of the collapse of the Taliban," said Nur Agha, a 22-year-old fighter.

Mohammad Afzal Amon, the commander of the opposition's elite Zarbati troops north of Kabul, said 600 troops had been sent to his area since the victory in Mazar-e-Sharif.

The loose coalition of opposition forces has said it intends to launch an offensive to take Kabul, but so far has not tried to move against heavily entrenched Taliban lines there. The Taliban headquarters is in the southern city of Kandahar.

Hemat, the Bakhtar chief, said Taliban troops were retreating from Mazar-e-Sharif toward Samangan province to the east and to Pul-e-Kumri in the southeast.

"Our troops still have high morale. They left to save the city from destruction," he said. The Taliban were sending reinforcements to its troops in the area, according to Hemat.

Mazar-e-Sharif has a large airport that could be refurbished for American and allied aircraft to conduct humanitarian missions and mount attacks against the Taliban. Uzbekistan is 45 miles to the north, and that supply route does not get blocked by winter snowfalls, a key concern for the opposition alliance.

The Associated Press contributed to this report.