Bin Laden supporters make they voices heard in Peshawar, Pakistan
"Osama is in Afghanistan, but he is at an unknown place for his safety and security," Mullah Abdul Salam Zaeef told reporters.
There has been a lukewarm response to the announcement in Washington, with White House spokesman Ken Lisaius saying it "does not change anything".
"The president was extremely clear... that the demands that he outlined were not open to negotiation nor were they open to debate," he added.
The Taleban ambassador said Washington could break the stalemate if it were willing to provide proof of Bin Laden's role.
"We say if they change and talk to us, and if they present evidence, we will respect their negotiations and that might change things."
However, the president of Pakistan, which has been negotiating with the Taleban, said that, although hopes were dim the Taleban would meet the US demands and hand him over, the "doors were open" for further negotiation.
"We are interacting with the Taleban to moderate their views in accordance with the dictates of the world opinion and we are still carrying on doing that," President Pervez Musharraf said in an interview on US television.
In other developments:
UK Prime Minister Tony Blair says he has been shown strong evidence linking Bin Laden to the attacks against the World Trade Center in New York and the Pentagon in Washington which cost more than 6,000 lives.
In a BBC interview, Mr Blair said the evidence from intelligence services was "powerful and incontrovertible".
Meanwhile in the US, President George W Bush is meeting key advisers at his Camp David presidential retreat to consider further the US response to the attacks that killed more than 6,000 people.
A BBC Washington correspondent says White House officials are drawing a picture of a president spending another weekend in intense discussion with his closest security advisors.
They say his message, repeated time and again, to those around him, is that nothing should deflect from the campaign to destroy terrorism.
However, Mr Bush has to deal with a weakening economy. He is understood to want to introduce a stimulus package next week that would increase unemployment benefits, tax cuts and the minimum wage.
Meanwhile, the FBI says it is following up over 100,000 leads.
More than a dozen British warships have arrived in the Gulf state of Oman, adding to speculation in the region that the US and Britain may launch military action soon.
'Nonsense'
Saudi Defence Minister Prince Sultan bin Abdul Aziz dismissed as "nonsense" reports that the Saudi authorities would allow Washington to use its bases to attack Afghanistan.
However, he did say Saudi airspace could still be used as his country's contribution.
"We do not accept the presence in our country of a single soldier at war with Muslims or Arabs," Prince Sultan said in comments published on Saudi Arabia's official Okaz newspaper on Sunday.
The BBC Middle East correspondent says this is the clearest indication yet of where Saudi Arabia stands over the western military build up in the Gulf.
The comments imply that American planes could fly over Saudi Arabia but not launch an attack from its territory.
There has been much confusion over how far Saudi Arabia would work with the US since the 11 September attacks.
Saudi officials have hitherto been reluctant to comment publicly, apparently fearful of a backlash if Afghan civilians are killed in any military action.
Osama Bin Laden's main aims include the removal of US forces from Saudi Arabia, which he says defiles Islam, and overthrowing the Saudi monarchy.