Ayman al-Zawahri, al-Qaeda's longtime No 2 and considered the network's operational head, also sought to cast a role for the terror group in the popular uprisings shaking Arab world.
"Today, praise God, America is not facing an individual, a group or a faction," he said, wearing a white robe and turban with an assault rifle leaned on a wall behind him. "It is facing a nation than is in revolt, having risen from its lethargy to a renaissance of jihad."
Al-Zawahri also heaped praise on bin Laden, who was killed in the May 2 raid by US Navy Seals in the Pakistani garrison town of Abbottabad. Al-Zawahri, who is believed to be operating from somewhere near the Pakistan-Afghanistan border, also criticised the US for burying bin Laden at sea.
"He went to his God as a martyr, the man who terrified American while alive and terrifies it in death, so much so that they trembled at the idea of his having tomb" he said.
Al-Zawahri - who referenced the toppling of rulers in Tunisia and Egypt and continued uprisings in Libya, Yemen and Syria - tried to cast recent developments as in line with his group's longtime goal: to destroy America and its allies. He said America now faces the international Muslim community.
First comment by potential successor
"Our brothers who are working in Islam in all places, I tell you that our hands are extended to you and our hearts are open to you, so that we can work together to make Allah's word the highest and to make Islamic law in Muslim lands the ruler, not the ruled," he said in a video released on militant websites.
Al-Qaeda has long sought to topple many of the Arab leaders whose regimes have been shaken or toppled by popular uprisings this year, though militant Islam has played next to no role in any of them and most activists say they seek civil, not religious rule.
Within days of the bin Laden raid, al-Qaeda had issued a statement vowing to keep fighting the United States, a message that was likely designed to convince followers that the organisation would remain vigorous and intact even after its founder's demise.
But al-Zawahri's eulogy was the first comment by one of his potential successors on bin Laden's killing.
He also said US officials withheld the release of photographs of bin Laden's body, fearing the "Islamic peoples' anger and hate" for America. He claimed bin Laden "achieved what he wanted to do, which is to incite the Islamic nation to holy war, and his message had reached all".
Al-Zawahri, who is Egyptian, is a less charismatic figure believed to lack bin Laden's ability to bring together the many nationalities and ethnic groups that make up al-Qaeda. His appointment as the next al-Qaeda leader could further fracture an organisation that is thought to be increasingly decentralised.
Anger towards Pakistan
The eulogy included five poems of praise for bin Laden, describing him alternately as a modest, noble and shrewd commander and "the vanguard of jihad against the communists and then the Crusaders", a reference to bin Laden's campaign in the Afghan war against the Soviets in the 1980s and the September 11 2011 attacks against the United States.
Al-Zawahri also vented his anger at Pakistani military leaders and politicians, implying they had a role in bin Laden's death.
"I call on the Pakistani nation to rise up against the mercenary military traitors and the corrupt politicians who turned Pakistan into an American colony, allowing it (America) to kill or capture whoever it wants," al-Zawahri said.
He concluded by saying bin Laden will remain a "source of horror and a nightmare chasing America, Israel and their allies".