Several experts said prevailing U.S. intelligence was at odds with that assertion as well.
Bruce Hoffman of Georgetown University, a veteran counter-terrorism analyst and government consultant, said the vast majority of fighters who are part of Al Qaeda in Iraq are Iraqis who have shown little interest in seeking targets beyond that country's borders.
In his speech, Bush acknowledged that the organization was one of several Sunni Muslim radical militant groups in Iraq, but that the intelligence community considered it to be the most dangerous because it was behind "most of the spectacular, high-casualty attacks," which were intended to accelerate sectarian violence.
Frank Hyland, a former consultant at the CIA's counter-terrorism center and at the multi-agency National Counterterrorism Center, said he agreed that Al Qaeda in Iraq was a dangerous organization with ties to Al Qaeda central in Pakistan.
But he added that Al Qaeda in Iraq was one of dozens of groups attacking civilians and U.S.-led troops in Iraq.
Other Sunni groups, Shiite Muslim militias such as the Al Mahdi army, criminal gangs, "throwaway kids" and Iranian intelligence operatives are doing so as well, he said.
A British panel of private and government experts known as the Iraq Commission released a report this month that concluded there were between 50 and 75 "disparate groups, formed to rid the country of coalition forces."
One of the more controversial claims that the Bush administration has made involves the operational link between Al Qaeda in Iraq and Al Qaeda's command-and-control operations headed by Bin Laden and others in Pakistan.
On Tuesday, Bush sought to bolster what he said were direct ties between the two, in response to criticism that the administration has been exaggerating the connections.
Bush said the founder of Al Qaeda in Iraq, the late Abu Musab Zarqawi, merged his organization with Al Qaeda and pledged allegiance to it.
Some experts and former U.S. intelligence officials said Tuesday that the Iraq group had always had its own agenda, as evidenced by a public fallout between Zarqawi and Al Qaeda's No. 2 leader, Ayman Zawahiri, over Zarqawi's killing of Shiite Muslims in Iraq.
Bush alluded to that disagreement in his speech, but he emphasized repeatedly that Al Qaeda in Iraq was part of Al Qaeda's "decentralized chain of command, not ... a separate group" and that the two operations were "united in their overarching strategy."