"I am responsible for assigning the roles of the 19 brothers who took part in the attacks of September 11, 2001," the voice said on the tape recording released on the As-Sahad website, frequently used for broadcasts by Al-Qaeda.
The man also claimed that Zacarias Moussaoui, sentenced to life imprisonment in the United States, had no role in the September 11 attacks.
It could not immediately be confirmed that the voice was indeed that of Bin Laden.
If confirmed, it would be one of the Al-Qaeda chief's clearest admissions of his role in organising the September 11th attacks on New York and Washington which killed almost 3,000 people.
Moussaoui, 37, is the only person charged in the United States over the terror attacks on the World Trade Centre and the Pentagon.
A US judge this month formally sentenced him to life imprisonment without parole for his role in the September 11 conspiracy, after a jury rejected the death penalty.
The jury ruled on May 3 that Moussaoui, a French citizen of Moroccan descent, should be imprisoned for life for failing to inform US authorities about what he knew of Al-Qaeda plans to carry out the September 11 attacks.