After a week of clashes, Afghanistan's battle against Taliban (search) insurgents intensified Friday with government soldiers meeting fierce resistance as they entered remote southern mountains believed to be a rebel stronghold.

Dozens of Taliban were killed in fighting as Afghan troops pushed into a deep gorge and along a mountain stream after a night of heavy U.S. bombing in the Chinaran and Larzab mountains of Dai Chupan district (search), an Afghan official said.

The U.S. military said one of its special operations soldiers died in a fall during a nighttime assault in the rugged mountains of southern Zabul province (search). His name was not immediately released. No casualties were reported among the Afghan soldiers.

From late Thursday until nearly dawn, U.S. warplanes pounded two suspected Taliban positions in the area, provincial intelligence chief Khalil Hotak told The Associated Press.

Then 500 Afghan soldiers moved in on the Taliban fighters, who had taken up fortified positions. Four Afghan soldiers were wounded in the fighting Thursday.

Hotak described the area as a Taliban stronghold, from which the insurgents direct their operations into the neighboring provinces of Kandahar (search), Ghazni and Uruzgan.

"The fighting was intense and we have inflicted heavy damage on the Taliban," Hotak said at a command center set up in Qalat, about 45 miles south of the fighting. "Our forces counted 35 Taliban bodies."

It was impossible to verify Hotak's account of the casualties and description of the area as a Taliban stronghold.

The U.S. military, meanwhile, announced the second fatality of a coalition soldier within 10 days in Afghanistan. Some 11,500 U.S.-led forces are helping Afghan troops in hunting down Taliban and Al Qaeda (search) fighters in the south and east of the country.

"The injuries were sustained during an accidental fall and were not the result of hostile action," the military said in a statement from Bagram Air Base, north of the capital Kabul.

On Aug. 20, a U.S. special operations soldier was killed in action in eastern Paktika province.

This week's fighting follows a surge in military action by the Taliban in recent weeks. Taliban fighters have been staging deadly attacks on Afghan forces, officials and aid workers, in an apparent bid to undermine the government of President Hamid Karzai, who took power soon after the Taliban's ouster by U.S.-led forces in 2001.

Hotak said his forces believe hundreds of Taliban have taken up positions in the area, with at least 15 hideouts, the largest being in a range called Hazar Buz, about four miles from the latest battle.

As he spoke, Hotak received calls from commanders at the scene and barked back orders. "We get information when the Taliban change their positions. Then we give this information to our commanders," he said.

Afghan officials say they believe at least two prominent Taliban commanders, Mullah Dadullah and Mullah Shafiq, were leading the fighting in the area. Hotak named a third: Mullah Abdul Qahar, a senior Taliban commander in the province during the Islamic militia's rule.

Haji Granai, an Afghan military commander, said at least two U.S. bombers and two helicopters helped in the operation, and Hotak said 20 American troops and 12 military vehicles were on the ground to aid the Afghan forces.