Bin Laden planned and supervised the attack that killed 23 people outside the big U.S. base at Bagram during Cheney's visit, said Mullah Dadullah, the Taliban's main military commander in southern Afghanistan who has had close associations with al Qaeda.
"You may remember the martyr operation inside the Bagram base, which targeted a senior U.S. official. ... That operation was the result of his wise planning. He (bin Laden) planned that operation and guided us through it. The operation was a success," Dadullah told Al-Jazeera.
He did not say how he knew that bin Laden planned the attack, and it was not immediately clear when the interview took place.
Dadullah also insisted that bin Laden was alive and well, according to the interview.
"Thank God he is alive. We get updated information about him. Thank God he planned operations in both Iraq and Afghanistan," Dadullah told Al-Jazeera in excerpts that were translated into Arabic.
The bombing killed about 20 Afghan civilians, a U.S. soldier, a U.S. contractor and a South Korean soldier outside Bagram while Cheney was meeting with officials inside the base, an attack the Taliban claimed was aimed at Cheney but which officials said posed no real threat to the vice president.
The attacker never tried to penetrate even the first of several U.S.-manned security checkpoints at Bagram, instead detonating himself among a group of Afghan workers outside the base.
The bearded Dadullah, wearing a black turban and a gray traditional Afghani robe, was interviewed by Al-Jazeera's correspondent in Afghanistan. In the interview, the Taliban commander was seen sitting on the ground in the middle of a field with some trees.
In the video, a man covering his head and face with a white scarf and wearing an ammunition belt can be seen in the background.
Parts of the interview were broadcast on Al-Jazeera's English and Arabic satellite TV channels and were posted the stations' Web sites.
Al-Jazeera, which is based in the Gulf Arab state of Qatar, said it planned to show the entire interview later Wednesday. The station declined to provide any more details about the interview.