Washington (CNN) -- Nearly a year after commandos killed Osama bin Laden at a compound northern Pakistan, U.S. officials "still have work to do" in order to defeat al Qaeda, a top counterterrorism official said Sunday.
"We're on a path to al Qaeda's destruction, and the president has committed that we're not going to rest until al Qaeda is destroyed as an organization in the Afghan-Pak area, as well as in other regions of the world," John Brennan, U.S. President Barack Obama's chief counterterrorism adviser, told CNN's "State of the Union."
Killing bin Laden and dismantling the terror group's infrastructure in areas of Pakistan and Afghanistan have been key steps, Brennan said.
Officials believe Ayman al-Zawahir, the longtime deputy of bin Laden who took over leadership of al Qaeda after his death, remains in that region, Brennan said.
"We believe he's in that region of the world, as well as other al Qaeda leaders that continue to borough into areas of...the Federally Administered Tribal Areas of Pakistan. That's why we're working very closely with our Pakistani partners," he said. "We're not going to relent until they're brought to justice one way or the other."
The United States also has its sights set on al Qaeda targets in Yemen and Africa, he said.
When asked about a new political ad featuring former President Bill Clinton praising Obama for the decision that led to bin Laden's death, Brennan, who also worked with the CIA for 25 years, stressed, "I don't do politics. I'm not a Democrat. I'm not a Republican."
"It was a tough decision. As we know, the evidence was not there as far as an iron-clad case. A lot of it was circumstantial," the counterterrorism adviser said. "I just know that President Obama, when the time came for him to make a momentous decision like that, he took the action that did bring bin Laden to justice."
Speaking to reporters Friday, U.S. Defense Secretary Leon Panetta said there was no "silver bullet" that would destroy al Qaeda.
"The way this works is that the more successful we are in taking down those that represent their spiritual and ideological leadership, the greater our ability to weaken their threat to this country," he said.
The FBI and the Department of Homeland Security last week warned of the possibility of terrorist attacks leading up to and after the anniversary of the May 2, 2011, killing of bin Laden. There is no specific, credible terror threat, the agencies said.
The warning, released by the FBI and DHS, says individuals have posted messages on "violent extremist Web forums" vowing attacks on the United States around the anniversary, but adds that "such threats are almost certainly aspirational."
On Sunday, Brennan said the United States has "reduced significantly" al Qaeda's "ability to carry out attacks against the homeland."
"Their ability has been degraded significantly, and our defenses have improved significantly also in the past decade, so their ability to carry out an attack here in the United States now, compared to 10 years ago, is significantly diminished," he said.