Bin Laden's hands mimicked the planes' impact
The video shows Bin Laden joking and laughing with friends and associates about the suicide plane attacks on New York's World Trade Center, in which more than 3,000 people died.
The US says the tape provides compelling evidence that Bin Laden was behind the 11 September attacks.
But the BBC's Middle East correspondent, Frank Gardner, says that at street level in the Arab world, many believe the tape is a fake, a PR gimmick dreamed up by the US administration.
Some mistrust the translation of Bin Laden's remarks, which was necessary as the recording is of both very poor audio and visual quality.
Pentagon officials asked four non-government Arabic speakers to listen to the remarks and agree on a uniform translation.
Our correspondent says some Saudis do not believe the man on the tape is really Bin Laden.
Taleban 'doubtful'
In Jordan, political analyst Labib Kamhawi said that even if the video is genuine, Bin Laden's praise for the attacks "does not prove that Bin Laden was responsible" for them.
A leading Saudi dissident in London, who asked not to be named, said he was sure the recording was genuine because of the language used and topics discussed.
The defence minister of the ousted Taleban regime in Afghanistan told the BBC that he was doubtful about the recording's authenticity, saying it was unlikely that Bin Laden would have been naive enough to say such things on a recording.
Pakistan's Government, meanwhile, said the broadcast of Bin Laden praising the attacks proved that Islamabad had made "the right decision" in supporting Washington in its military campaign.
Our correspondent adds that the tape is unlikely to win support from many ordinary Arabs because it has been released as Israeli-Palestinian violence increases.
Many in the Arab world are angry at the US as a backer of Israel.
Advance knowledge
In the video, Bin Laden, relaxing in green military jacket and white head-dress, claims to have known the attacks would take place five days in advance, and says the destruction of the twin towers exceeded his expectations.
American intelligence officers are said to have recovered the tape from a house in the eastern Afghan town of Jalalabad following the collapse of the ruling Taleban, who were harbouring Bin Laden.
Bin Laden identifies Mohamed Atta, suspected of hijacking the first plane, as the group's leader.
In one section of the videotape, the Saudi-born militant suggests that some of the hijackers did not know what their mission would be.
"The brothers who conducted the operation, all they knew was that they have a martyrdom operation and we asked each of them to go to America, but they didn't know anything about the operation, not even one letter," he said.
Bin Laden is seen in the video with the number two in the al-Qaeda network, Ayman al-Zawahri, and a spokesman, Abu Ghaith, in what the Pentagon says is a guest house in Kandahar, in southern Afghanistan.
Optimism
Bin Laden said that before the attacks on the World Trade Center, he and his men were estimating how many people would be killed.
"We calculated that the floors that would be hit would be three or four floors," he said, gesturing with his hands to show a building and a plane flying into it.
"I was the most optimistic of them all," he said.
He also claimed to have known the attackers were ready.
"We had notification since the previous Thursday that the event would take place that day," he said, chuckling.
He then described hearing the news reports with his aides.
"They were overjoyed when the first plane hit the building, so I said to them: Be patient," he said with a smile.
The BBC's Katty Kay says the White House hopes the video will bolster international support for the war on terrorism.
"For those who see this tape, they'll realise that not only is he guilty of incredible murder, he has no conscience and no soul, that he represents the worst of civilisation," said President George W Bush.