Hundreds of al-Qaeda militants are reported to be on the run.
"We cleared al-Qaeda from our land. We did the job," senior commander Haji Mohammad Zaman told reporters.
In Washington, US Secretary of State Colin Powell said they had no reason to believe the al-Qaeda leader was either killed or captured, but he admitted they did not know where he was.
The reported victory comes after weeks of fighting and relentless bombing, with US warplanes dropping hundreds of bombs on al-Qaeda positions in the past couple of days alone.
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Another local commander, Hazrat Ali, beamed as he told the BBC that they had killed about 200 al-Qaeda fighters, and captured another 35.
He said 500 al-Qaeda members were on the run in the forests, without cover, and would be pursued.
His men, he said, were searching the area "metre by metre."
Local people have been warned that anyone sheltering them will face death.
"Anyone who paves the way for al-Qaeda forces to live in the White Mountains will be given capital punishment," Hazrat Ali said.
In other developments:
Bin Laden's voice
The defeat of al-Qaeda on Afghan soil has, however, done nothing to resolve the mystery of Osama Bin Laden's whereabouts.
"Osama Bin Laden is not here," tribal commander Haji Zaman said.
An unconfirmed report from Washington said Bin Laden had been heard giving orders over a short-range radio in the Tora Bora mountains over the past week.
A US official, speaking on condition of anonymity, said it was confirmed "with reasonable certainty" that the voice on the radio was Bin Laden's, after it was compared with several videotapes.
The US blames Bin Laden for the 11 September attacks on the World Trade Center and the Pentagon.
Hot pursuit
Speaking in Washington, US Secretary of State Colin Powell said it appeard that the al-Qaeda network was defeated.
"Al-Qaeda is being destroyed in Afghanistan. Now we have to destroy it wherever it exists around the world," Mr Powell said.
Mr Powell admitted that they did not know whether Osama Bin Laden was still in Afghanistan or had escaped into Pakistan, but that he was being hotly pursued.
"We will get Bin Laden, whether it's today or tomorrow," he said.
And in Kabul, where he was making a lightning visit, US Defence Secretary Donald Rumsfeld cautioned against anticipating victory.
"There are people trying to escape but that gets harder as night falls. The question is does that mean it's almost over in that area and I doubt it," Mr Rumsfeld said, quoted by Reuters news agency.