It was the first footage of bin Laden to appear in more than a year and came just days before voters head to the polls Tuesday after an extremely tight president race.
In the 18-minute tape, bin Laden, who appeared to be sitting or standing at a table against a neutral background, said: "Despite entering the fourth year after Sept. 11, Bush is still deceiving you and hiding the truth from you and therefore the reasons are still there to repeat what happened."
Bin Laden said he thought of the method of attacking U.S. skyscrapers when he saw Israeli aircraft bombing tower blocks in Lebanon in 1982.
"We decided to destroy towers in America," he said. "God knows that it had not occurred to our mind to attack the towers, but after our patience ran out and we saw the injustice and inflexibility of the American-Israeli alliance toward our people in Palestine and Lebanon, this came to my mind."
Although there was no way to authenticate the tape or say when it was made, it referenced the upcoming presidential election.
"Your security is not in the hands of (Democratic candidate John) Kerry or Bush or al-Qaida. Your security is in your own hands," bin Laden said, according to the Associated Press.
"To the U.S. people, my talk is to you about the best way to avoid another disaster. I tell you: Security is an important element of human life and free people do not give up their security.
"If Bush says we hate freedom, let him tell us why we didn't attack Sweden, for example. It is known that those who hate freedom do not have dignified souls, like those of the 19 blessed ones," he said, referring to the 19 hijackers.
"We fought you because we are free ... and want to regain freedom for our nation. As you undermine our security, we undermine yours."
An editor at Al-Jazeera said the network received the tape Friday but did not say how, Reuters reported.
In September 2003, Al-Jazeera aired a tape of bin Laden with his deputy Ayman al-Zawahiri in which he mentions five Sept. 11 hijackers by name.
An audiotape, which CIA analysts said was likely bin Laden, surfaced in April and called for a truce with European nations if they pulled troops out of Muslim countries.