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The key challenge for the West over the next few years will be to balance aggressive counterterrorism operations against the risk of galvanizing new fronts for the terrorist movement, Mr. Cardillo said.

One such front is in Syria, where officials say al Qaeda in Iraq is trying to make inroads in the popular uprising against President Bashar Assad’s autocratic regime.

Little support in Arab world

Al Qaeda is interested in not only affecting the result, but in contributing to the fighting,” a senior U.S. counterterrorism official said.

However, the official said the terrorist movement has made few strides among Arab Spring protesters who have sought to overthrow longtime dictatorships - including in Syria, where there are few obvious sympathizers to al Qaeda’s cause.

A recent poll conducted as part of the Pew Research Center’s Global Attitudes Project found overwhelmingly unfavorable views of al Qaeda in Egypt, where Hosni Mubarak stepped down as president last year after a popular uprising.

Negative views of the terrorist network also were found in Jordan, Turkey, Lebanon and areas of Pakistan, where bin Laden was killed in hiding in May 2011.

“As these new governments take real steps to address public demands for political participation and democratic institutions and remain committed to [counterterrorism] efforts, we judge that core al Qaeda and the global jihadist movement will experience a strategic setback,” Mr. Cardillo said.

He warned, however, that any prolonged instability or missed promises by the new governments would give al Qaeda and its affiliates more time to establish networks, attract support and potentially engage in operations with less scrutiny from local security services.

Within U.S. borders, officials said, a mass attack by a foreign group using chemical, biological, radiological or nuclear weapons would be unlikely within the next year but the threat would come from “lone wolf” attackers or small groups not formally affiliated with al Qaeda but inspired by its ideology.

“It’s more than just one person. It’s an idea. It’s a concept, and it’s a concept that exists in many parts of the broader world today,” said Michael O’Hanlon, senior fellow at the Brookings Institution.

While officials say al Qaeda’s new leader, Ayman al-Zawahri, is not as inspirational as bin Laden, it is much too early to count out core al Qaeda.

Al Qaeda is a resilient organization that’s faced incredible difficulties in the past after leaving Afghanistan,” the senior U.S. counterterrorism official said. “It was patient. It managed to wait us out, and they’re clearly attempting to do that again right now.”

“Despite the great progress we’ve made against al Qaeda, it would be a mistake to believe this threat has passed,” Mr. Brennan said.