The al-Qaida chief made the proposal in an audiotape broadcast by Aljazeera, and authenticated by the CIA, in which Bin Laden warned of pending attacks in the heartland of the United States.
But he also offered a long-term truce if Washington withdrew its military presence from Iraq and Afghanistan - the latter his former safe haven until US forces ousted his Taliban allies after the September 11 attacks.
Dick Cheney, the US vice-president, on Thursday said the message showed that the al-Qaida network had been driven underground and was now unable to produce video messages, but warned the group was still lethal.
Asked about Bin Laden's truce offer, Cheney told Fox News Channel that it sounded like a ploy.
"This is not an organisation that is ever going to sit down and sign a truce," he said. "I think you have to destroy them. It's the only way to deal with them."
While the vice-president did not vouch for the authenticity of the tape, Central Intelligence Agency (CIA) analysts believe it was Bin Laden's voice on the tape, according to a CIA official who requested anonymity.
Cheney characterised Bin Laden's
truce offer as a ploy
Bin Laden, whom some US intelligence officials say is holed up in a remote mountainous region on the border between Afghanistan and Pakistan, had not been heard from since another recorded message in December 2004.
In April 2004, a few weeks after the Madrid train bombings that killed 191 people, Bin Laden in a video message also offered a truce to Europeans if they stopped attacking Muslims.
US officials were unsure when the latest message had been recorded, and Cheney said another question was whether it had been "pieced together" from past statements.
Asked whether killing Bin Laden would lessen the threat from al-Qaida, Cheney said "we'd still have problems" with the network because it does not rely on a centralised leadership.
Cheney also warned in a speech right as Bin Laden's message was broadcast that while "the enemy that struck on 9/11 is weakened and fractured, it is still lethal".
"Obviously no one can guarantee that we won't be hit again, but our nation has been protected by more than luck," he said in a reference to the avalanche of security measures imposed after 11 September in every major US city.
"It is no accident that we have not been hit for more than four years," Cheney added.
"It is no accident that we have not been hit for more than four years"
While some of Bush's Republicans and many opposition Democrats have criticised some of those measures, there was unanimity in rejecting any talk of a truce with al-Qaida across the US political landscape.
Scott McClellan, the White House spokesman, said: "We do not negotiate with terrorists. We put them out of business. We must not stop until they are defeated.
"The terrorists started this war. And the president made it clear that we will end it at a time and place of our choosing."
Democratic party chairman Howard Dean told Fox News: "You don't negotiate with terrorists. These people have killed 3000 Americans, there is no truce with al-Qaida, and there never will be. You can't trust them."