The confirmation came as newly uncovered documents found in bin Laden's residence revealed al-Qaida plans for derailing an American train on the upcoming 10th anniversary of the Sept. 11 attacks.
Terror experts have said bin Laden's death on Monday was a setback for al-Qaida but the threat of attacks remains and could even spike in coming days from individuals or small extremist groups inspired to take revenge for the killing.
The statement, dated Tuesday but posted Friday on militant websites, opens the way for the group to name a successor to bin Laden. His deputy Ayman al-Zawahri is now the most prominent figure in the group and a likely contender to take his place.
"The blood of the holy warrior sheik, Osama bin Laden, God bless him, is too precious to us and to all Muslims to go in vain," the statement said. "We will remain, God willing, a curse chasing the Americans and their agents, following them outside and inside their countries."
"Soon, God willing, their happiness will turn to sadness," it said, "their blood will be mingled with their tears."
The group gave no indication how it will retaliate. But separate details emerged Friday showing that bin Laden was scheming how to hit the United States hard again.
Materials confiscated by the Navy SEALs who killed the al-Qaida leader in Abbotabad, Pakistan, reveal the rail attack planning as of February 2010. One idea outlined in handwritten notes was to tamper with an unspecified U.S. rail track so that a train would fall off the track at a valley or a bridge.
Counterterrorism officials said they believe the plot was only in the initial planning stages. The FBI and Homeland Security issued an intelligence bulletin with details of the plan to law enforcement around the country. The bulletin, marked "for official use only," was obtained by The Associated Press.
Rather than making vehement cries of vengeance, the al-Qaida statement - entitled "You lived as a good man, you died as a martyr" - struck a tone of calmness and continuation. Though it included praise of bin Laden, much of the 11-paragraph statement was dedicated to underlining that al-Qaida would live on, depicting him as just another in a line of "martyrs" from the group.
"It is impossible, impossible. Sheik Osama didn't build an organization to die when he dies," the statement read. "The university of faith, Quran and jihad from which bin Laden graduated will not close its doors," it added.
"The soldiers of Islam will continue in groups and united, plotting and planning without getting bored, tired, with determination, without giving up until striking a blow," the statement.
It said bin Laden was killed "along an established path followed by the best of those who came before him and those who will come after him."
In the statement, al-Qaida also called on Pakistanis to rise up in revolt against its leaders to "cleanse the shame." It also said that an audio message bin Laden recorded a week before his death would be issued soon.
The writers of the statement appeared unaware of the announcement by American officials that bin Laden's body had been buried at sea. The statement warned against mishandling or mistreating bin Laden's body and demanded that be handed over to his family, saying "any harm (to the body) will open more doors of evil, and there will be no one to blame but yourselves."
The statement's authenticity could not be independently confirmed, but it was posted on websites where the group traditionally puts out its messages.
Reaction in the Islamic world to bin Laden's death has been relatively muted compared with the rage that he long inspired, raising questions about his relevance in a region that has been changed by a wave of pro-democracy uprisings.
On Friday, hundreds of members of radical Islamic parties protested in several Pakistan cities against the American raid and in favor of bin Laden. Many of the people chanted "Osama is alive" and blasted the U.S. for violating the country's sovereignty.
The largest rally took place in the town of Khuchlak in southwestern Baluchistan province, where about 500 people attended.
"America is celebrating Osama bin Laden's killing, but it will be a temporary celebration," said Abdullah Sittar Chishti, a member of the Jamiat Ulema Islam party who attended the rally in Khuchlak. "After the martyrdom of Osama, billions, trillions of Osamas will be born."