The United States will aim to destroy al Qaeda's central organization now that its leader Osama bin Laden has been killed and its capabilities degraded by U.S. operations, a top White House adviser said on Tuesday.

Since the 2001 attacks on New York and Washington, al Qaeda has spawned affiliated groups in the Middle East and North Africa and inspired attacks by so-called home-grown militants in Europe and the United States.

But White House counterterrorism chief John Brennan said bin Laden's death was the latest in a series of U.S. operations that have delivered "severe body blows" to al Qaeda's central network in Pakistan and Afghanistan over the past year.

"We're going to try to take advantage of this opportunity we have now with the death of al Qaeda's leader, bin Laden, to ensure that we're able to destroy that organization," Brennan told NBC's Today show. "We're determined to do so and we believe we can."

"We believe that we have damaged the organization, degraded its capability and made it much more difficult for it to operate inside of Pakistan as well as beyond."

Senate Foreign Relations Committee Chairman John Kerry said in an MSNBC interview on Monday that U.S. drone strikes in Pakistan's Federally Administered Tribal Areas had killed as many as 17 senior al Qaeda leaders before bin Laden's death.

Brennan spoke a day after world leaders and security experts urged increased vigilance against possible retaliatory strikes by al Qaeda.

CIA director Leon Panetta warned on Monday that bin Laden's death would "almost certainly" prompt his Islamist supporters to attempt some sort of retaliation.

But Brennan said U.S. officials were aware of no specific threat, nearly 48 hours after bin Laden's death.

"But what we're doing is, we're taking all those prudent measures that we need to whenever there's an incident of significance like this," Brennan said in a separate interview on ABC's "Good Morning America."

"Right now, I think we feel pretty confident that we are at the right posture."