The Taliban says it is ready to discuss handing over Osama bin Laden if the bombing stops.
The Deputy Prime Minister says the Taliban is ready to extradite him to a third country.
But he says the Taliban will need to see evidence linking bin Laden to the September 11 attacks.
"If the Taliban is given evidence that Osama bin Laden is involved" and the bombing campaign stopped, "we would be ready to hand him over to a third country," said Haji Abdul Kabir.
But he added, that the country would have to be one that would never "come under pressure from the United States."
Kabir urged the US to halt the air campaign, now in its eighth day, and open negotiations.
"If America were to step back from the current policy, then we could negotiate," he said. "Then we could discuss which third country."
Before the start of the air campaign, the Taliban had demanded evidence of bin Laden's involvement in the attack and had offered to try him before an Islamic court inside Afghanistan - proposals which the US promptly rejected.
Even though Kabir's statement does not mark a breakthrough, the fact that the Taliban is showing some flexibility at this time is significant in the wake of a week of punishing air strikes.