At the heart of the debate is the reality that whatever the continued ability of Al Qaeda or regional groups bearing its name to inflict damage on local or American interests, the terrifying power of its name has also given it a spectral second life as a kind of catchall for Islamist militants. Far-flung militants with little connection to the original group find the use of its name an easy way to exaggerate their threat, and politicians eager to campaign against them — whether in the United States Congress or Arab capitals — share that incentive.

“It is a ghost,” said Fahmy Howeidy, an Egyptian commentator. “People here don’t believe that Al Qaeda is this huge scary thing that is moving everywhere and behind everything in the whole world. They think that is American propaganda.”

Secretary of State Hillary Rodham Clinton said Tuesday that there were no intelligence warnings that an attack was imminent. She said that F.B.I. investigators had arrived in Tripoli and that the United States, with the Libyan authorities, would find those responsible. She did not discuss any potential ties to Al Qaeda, but blamed extremists opposed to the democratic changes in places like Libya, Tunisia and Egypt for the violence and protests around the region generally.

For political leaders in the United States or the Arab world, both addressing audiences that may have little familiarity with the various schools of ultraconservative or militant Islam, “the big name — Al Qaeda — can mobilize people,” said Diaa Rashwan, an expert on Islamist movements at the state-funded Al-Ahram Center for Political and Strategic Studies in Cairo. “It is very difficult to use another name that people don’t know when you already have this brand.”

“Al Qaeda as an organization, as a command, it doesn’t exist,” Mr. Rashwan said. “There are no orders from Ayman Zawahri coming to jihadists in Libya or Sinai to make something,” though he added, “Since the death of Osama bin Laden, Al Qaeda has been in a sense reborn because some of its ideas and the model have inspired new militants.”