The attack killed 23 people although Cheney escaped unhurt.
“Though we are sad for his loss, he left a legacy that will inflame the enemy nation and religion,” said the statement on Ekhlaas.org, which is frequently used by Islamist groups to convey their messages.
“We congratulate the Islamic nation for the martyrdom of the sheik, the lion, Abu Laith al-Libi.”
Asked by Reuters whether al-Libi had been killed, a senior US defence official in Washington said simply: “Yes.”
Another Western intelligence official who also declined to be named told the news agency: “At this point, there is no reason to doubt that he is dead.”
It was not immediately clear if al-Libi’s death was linked to a suspected US missile strike on Monday that killed up to 13 foreign fighters in Pakistan’s North Waziristan region.
Pakistani officials have yet to confirm al-Libi’s death, saying they were trying to gather details about the missile attack on the village outside of Mir Ali, the second-largest town in the northern region.
At least 12 people including Arabs, Turkmen from central Asia and local Taliban members were killed in Monday’s attack about four kilometres outside Mir Ali, intelligence officials and local eyewitnesses said.
Difficult to identify
One intelligence official in the area, speaking to the Associated Press on condition of anonymity, said the bodies of those killed were badly mangled by the force of the explosion and it was difficult to identify them.
US officials say Mir Ali was known to have a large concentration of foreign fighters, including a large group of mostly al-Qaeda-linked Uzbeks who fled to the tribal regions after the Taliban’s fall in Afghanistan in 2001.
In November al-Libi appeared in a video with Ayman al-Zawahri, al-Qaeda’s second-in-command, to announce that a Libyan Islamist group had joined the network.
Islamist websites have carried messages from al-Libi, including one in May in which he said al-Qaeda in Afghanistan was willing to exchange prisoners with Britain and other Western countries.