Among those groups, Mueller says, is the Pakistani militant organization Lashkar-e-Taiba, which he says is responsible for last November's attack in Mumbai, India, that killed 166 people.
Al-Qaeda-affiliated groups in Yemen claimed responsibility for two strikes against the U.S. Embassy in Sana last year. One was a coordinated assault last September that killed 17 people, including the six attackers.
"These guys think in terms of decades and centuries," says Phil Mudd, executive assistant director of the FBI's National Security Branch. "The challenge is whether you can keep the pressure on.
"… It's a shark's mouth," he says of al-Qaeda's resiliency. "You have to keep taking the teeth out again, and again. You can't allow the teeth to rotate to the front."
Not since al-Qaeda (Arabic for 'The Base') was formed 21 years ago after the Soviet Union's invasion of Afghanistan has the terrorist group faced so many questions about its viability, federal officials and analysts say.
It survived the destruction of its training bases. Yet the group's losses, especially the recent killings of senior al-Qaeda operatives, have created gaping holes in the "shark's mouth."
Among those killed by U.S. forces and allies:
• Rashid Rauf, mastermind of a failed 2006 plot to blow up trans-Atlantic airliners;
• Abu Khabab al-Masri, al-Qaeda's explosives expert;
• Usama al-Kini, linked by the FBI to the 2008 Marriott Hotel bombing in Islamabad that killed more than 60 people, including two Americans;
• Sheik Ahmed Salim Swedan, linked by the FBI to the 1998 bombings of the U.S. embassies in Kenya and Tanzania. The attacks killed 224 people, including 12 Americans.
"Al-Qaeda has taken more of a beating in the past year than at any time in the past five years," says Georgetown University professor Bruce Hoffman, who has examined terrorism for three decades. "But I haven't seen anyone deliver the knockout blow."
One of the reasons for the group's survival, Hoffman says, is its ability to adapt to pressure from U.S. and other forces.
Al-Qaeda's 20th anniversary last year was a reminder to its foes and followers that the group has created a lasting "brand," Hoffman says. At 20, al-Qaeda crossed a threshold formerly reached by terror groups such as the communist Revolutionary Armed Forces of Colombia, or FARC, Hezbollah in Lebanon and the Palestinian militant group Hamas. Even with bin Laden and Zawahri in seclusion, al-Qaeda has inspired new followers.
"Their greatest threat is in drawing people with clean Western passports" to become part of plots, Hoffman says, adding that there is recent evidence that up to 150 such Western converts have been attracted to al-Qaeda's ranks. "You're talking about people with the ability to fly under the radar (of terror profilers) with great ease."
But Sageman, the former CIA officer who last year was an adviser to New York's police department, believes al-Qaeda is closer to its end than a resurgence.
Not since the coordinated attacks on the London transit system, Sageman says, has the terrorist group shown the capability to strike targets in the West. The July 7, 2005, bombings of the subway and bus systems killed 56 people, including four bombers, and injured 700 others.
"Al-Qaeda has not been responsible for a single scratch (in the West) in more than four years," Sageman says. "Their training and leadership is a disaster." He says groups inspired by al-Qaeda are "mostly involved in local insurgencies."