U.S. jets bombed Al Qaeda positions in eastern Afghanistan's White Mountains throughout the day Sunday. A senior commander with anti-Taliban forces attacking those positions from the ground warned the fight will not be easy.

No one knows for sure, but local commanders believe there are more than 1,000 Al Qaeda fighters holed up in the mountains, using cave complexes built by anti-Soviet guerrillas with U.S. funding during the 1980s. Mohammed Zaman, defense chief for the eastern alliance, said Sunday he was certain Osama bin Laden is with them.

"He is still there. He has not escaped and we will do everything possible to make sure he doesn't escape," Zaman said on the front line.

Others in Afghanistan believe bin Laden, the prime suspect in the Sept. 11 terrorist attacks, is hiding elsewhere in the country. All the reports are based on speculation, and rumors of bin Laden sightings are common.

U.S. B-52 bombers made repeated passes over the Al Qaeda positions Sunday, dropping four to 10 bombs each time in an effort to soften their defenses so ground troops can move in. Hundreds of eastern alliance fighters watched from several miles away as plumes of brown smoke and dust filled mountain valleys.

As a U.S. Navy P-3 Orion reconnaissance plane buzzed overhead, a fighter jet made a pass, dropping a 2,000-pound bomb onto what appeared to be a cave in the side of a mountain ridge, producing a brilliant orange flash, black smoke and a percussive boom across the valley.

Zaman said three of his men were killed after they captured a strategic mountain peak Saturday night. He said 50 of his men had fought up the mountain, only to be hit by a U.S. airstrike.

But overall, Zaman said the U.S. airstrikes were critical to the success of his ground assault on the Tora Bora and Milawa valleys, where the Al Qaeda forces have reinforced fighting positions and are hiding in cave complexes that penetrate as much as 1,150 feet into the mountain.

"This is not going to be an easy battle. These valleys are very complicated, there are many hills, small caves and large boulders," Zaman said. He said his soldiers from the Eastern Shura, or council, had surrounded the al-Qaida forces and that there was no way for them to escape or be resupplied.

But the Al Qaeda forces, who are living in the caves with their wives and children, have had five years to reinforce the Tora Bora and Milawa cave systems and stock them with months of rations, Zaman said. Al Qaeda's trench and cave system, combined with well-fortified mortar positions, are very resistant to bombing and overlook every approach to the valley, he said.

Zhavez Nadar, 27, who has been among the troops probing the al-Qaida defenses, said so far they are strong, despite weeks of bombing.

"We have made a front line on Milawa, and (Al Qaeda) keeps changing their positions," Nadar said. "If we attack now, we could face defeat. We've attacked before and they've pushed us back every time so far. We have failed to take the area."

Zaman said Al Qaeda has much heavier weaponry than they have used so far, including 120mm mortars and multiple rocket launchers. He said Al Qaeda leaders keep sending messages, via villagers who live in the area or over loudspeakers, that they don't want to fight fellow Muslims, urging the Afghans to send American soldiers instead.

"They are waiting for the American, British and French soldiers to come and fight," Zaman said. "They would be very happy to fight American soldiers."