And in a sign that the Pakistani government is washing its hands of the Taliban's fate, Pakistan declared that Afghanistan's Taliban rulers "don't have much time" to stave off military strikes.
Prime Minister Tony Blair's emotional speech to his annual Labor Party conference was the toughest warning yet by a European leader.
"The Taliban aid and abet him. He will not desist from further attacks, they will not stop helping him," he said, referring to bin Laden.
"We stated the ultimatum. They haven't responded.
"I say to the Taliban: Surrender the terrorists or surrender power. It's your choice," Blair said.
Blair stopped short of declaring that military strikes against Afghanistan were inevitable while stressing that any such strikes would be "proportionate, targeted" and would be launched with avoiding civilian casualties in mind.
"We are not the ones who waged war on the innocent. We seek the guilty," he said.
"Be in no doubt, bin Laden and his people organized this atrocity," the prime minister said. Several hundred Britons are presumed dead in the attacks.
"Whatever the dangers of the action we take, the dangers of inaction are far, far greater," Blair said.
The Taliban ambassador to Pakistan, Abdul Salam Zaeef, dismissed the threats by the United States and its allies, saying, "We don't want to surrender [bin Laden] without any proof, any evidence."
He also dismissed NATO's claims that Washington had presented the alliance with conclusive evidence.
"If they are giving it [evidence] to the other countries, it belongs to them, not to us," he replied. "They haven't given it to us."
In his speech, Blair sought to reassure members of the Labor Party that humanitarian aid would be as important as military strikes. He called the aftermath of the attacks in the United States a chance to "reorder this world around us."
"There is a coming together," he said. "The power of community is asserting itself. We are realizing how fragile are our frontiers in the face of the world's new challenges."
He called for campaigns to lift Africa out of poverty and halt climate change and said the world would not abandon Afghanistan once the Taliban regime was removed from power.
Jack Straw, Blair's foreign secretary, accused opponents of action against terrorism of acting like those who sought to appease the Nazis in the 1930s.