"This latest statement is a clear admission of responsibility for the terrorist attacks in the US of September 11," said the office of British Prime Minister Tony Blair.
"It can leave no one in any doubt of Osama bin Laden and al Qaeda's intention to continue to conduct, incite and support acts of terrorism."
President George W. Bush had earlier said the US Government was taking "strong precautions" to safeguard Americans against terror attacks. The FBI has warned that more attacks are possible in the coming days.
CNN and other major US television networks delayed broadcast of the al Qaeda statement and instead used excerpts, in accordance with a request by the Bush Administration.
White House officials have told media organisations that the group's statements might contain coded messages to bin Laden's followers to carry out fresh attacks on US targets.
In his weekly radio address, Bush declared the first phase of the military campaign against bin Laden a success, saying a week of bombing had disrupted "the terrorist network inside Afghanistan".
"American forces dominate the skies over Afghanistan and we will use that dominance to make sure terrorists can no longer freely use Afghanistan as a base of operations," said Bush.
- REUTERS
Map: Opposing forces in the war against terror
Afghanistan facts and links
Full coverage: Terror in America