A statement by the White House said Bin Laden - the prime suspect in last week's attacks on New York and Washington - should be turned over to "responsible authorities".
It followed US demands for him to be handed over, and a statement by the ruling Taleban's spiritual leader that he would not be extradited.
But White House spokesman Ari Fleischer said the resolution was not enough to satisfy the Bush administration.
"It does not meet America's requirements," he told reporters. "This is about much more than one man being allowed to leave voluntarily, presumably from one safe harbour to another safe harbour.
"The president has demanded that key
figures of the al-Qaeda terrorist organisation, including Osama Bin Laden, be turned over to responsible authorities and that the Taleban close terrorist camps in Afghanistan - and the United
States stands behind those demands."
Pakistan Foreign Minister Abdul Sattar said the Taleban offer was significant but "not a big step forward".
Pakistan had sent a mission to the Taleban in a failed effort to persuade them to hand Bin Laden over.
Holy war threat
The Taleban clerics also passed a resolution that called for a jihad, or holy war, in response to any US attack on Afghanistan.
The US, which has begun a major military build-up in the Gulf, has threatened to attack if the Taleban allow Bin Laden to remain in Afghanistan.
Religious leaders in Kabul had said the Taleban would be asked to persuade Bin Laden to leave Afghanistan at the proper time and of his own volition.
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"To avoid the current tumult... and also future similar suspicions, the high council of the honourable ulema [religious scholars] recommends to the Islamic Emirate [of Afghanistan] to persuade Osama Bin Laden to leave Afghanistan whenever possible," said the resolution.
The decision came as a surprise, as the mood at the meeting had appeared to be in favour of Bin Laden, and most believed the clerics would recommend he should be allowed to stay.
A guest of the Taleban since 1996, he has offered to leave Afghanistan once before, in 1998, after the attacks - also blamed on him - on US embassies in Kenya and Tanzania.
But the BBC's Susannah Price says that if Bin Laden decided to leave now, he would have few options open to him as no other country would want to face the threat of US attacks.
The reclusive Taleban leader Mullah Mohammad Omar on Wednesday dismissed US allegations against Bin Laden as an excuse to wage war on Islam.
In a statement from his base in the city of Kandahar, he said: "Islam is a true way of life and our enemies and those against our religion believe that we are their enemies.
The Taleban's deputy ambassador in Islamabad also said on Thursday that Bin Laden was ready to stand trial in Kabul, or in another Muslim country.
Suhail Shaheen told Reuters: "If there's evidence, he is ready for a trial.
"He said 'I am not involved, I am a guest (in Afghanistan). If they have evidence, I am ready'."
Starvation fears
Pakistan, until now the ruling Taleban's main backer, has agreed to help the US in its efforts to track down and punish the perpetrators of last week's attacks.
But the decision has caused fury among Islamic militants, with protests growing daily.
President Pervez Musharraf warned on Thursday that Pakistan was threatened with destruction.
Fears of a US strike and a food crisis caused by drought have forced more than 1 million people to leave their homes, says the UN.
Reports that the Taleban have been rounding up young men to fight a holy war against the United States have contributed to the exodus.