US President George W Bush has rejected the latest Taliban offer to hand over Osama bin Laden.
The Taliban Deputy Prime Minister says evidence must be produced linking bin Laden to the September 11 attacks.
But a White House spokesman says the president has made clear there will be no negotiations.
Deputy PM Haji Abdul Kabir said that "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".
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."
But White House spokeswoman Anne Womack said: "The president has been very clear, there will be no negotiations."
Kabir's offer came a day after the Taliban's supreme leader rebuffed a "second chance" given by Bush for the Islamic militia to surrender bin Laden.
Mullah Mohammed Omar said there was no move to "hand over anyone".