Panetta’s assessment could stoke the debate in Washington over how soon to pull the U.S. military from the land where Osama bin Laden’s network launched the attacks of Sept. 11, 2001, against the United States. Some question why a continued military commitment is necessary if al-Qaida’s end is in sight, given that it was the reason the U.S. began the war.

Although not as specific as Panetta about what it will take to break al-Qaida, the top American commander in Afghanistan said in a separate interview that he agrees the group is on the ropes.

“There has been enormous damage done to al-Qaida” beyond bin Laden’s killing May 2 in Pakistan. Army Gen. David Petraeus said. “That has very significantly disrupted their efforts and it does hold the prospect of a strategic defeat, if you will, a strategic dismantling, of al-Qaida.”

Panetta said he hoped his shift from CIA director to defense secretary, combined with a change of U.S. civilian and military leaders in Kabul, will put the troubled U.S.-Afghan relationship “back on the right track.”

Mixed with the optimism was a hint of concern about resetting the Obama administration’s increasingly rocky relationship with Afghan President Hamid Karzai. He frequently criticizes the U.S. military and is known to offer what American officials see as weak support for his own fledgling army and police.

Panetta pointedly noted that the U.S. feels compelled to deal with “a lot of leaders throughout the world who have problems … and that’s the situation here. We have to respect him as president of his country.”

Panetta had dinner with Karzai but they did not hold a joint news conference, as is customary when an American defense secretary visits the capital.

In the aftermath of bin Laden’s death and apparently with the benefit of new intelligence gained in the raid on his compound, the U.S. has determined that eliminating “somewhere around 10 to 20 key leaders” of al-Qaida would cripple the network, Panetta said. Those leaders are in Pakistan, Yemen, Somalia and North Africa, he said.

“We’re within reach of strategically defeating al-Qaida,” Panetta said, addressing reporters for the first time since succeeding Robert Gates as defense secretary July 1.

Asked why he feels confident about wiping out al-Qaida, Panetta said, “The key is that having gotten bin Laden, we’ve now identified some of the key leadership within al-Qaida both in Pakistan as well as in Yemen and other areas.”

He named only two of the leaders on the list:

—Ayman al-Zawahri, bin Laden’s designator successor. Panetta said the U.S. believes al-Zawahri is living in the Federally Administered Tribal Areas of western Pakistan.

—Anwar al-Awlaki, the U.S.-born Muslim cleric living in Yemen. The U.S. has put him on a kill-or-capture list.

“If we can be successful at going after them,” he said, referring to the 10 to 20 leaders, “I think we can really undermine their ability to do any kind of planning, to be able to conduct any kind of attack” on the United States. “That’s why I think it’s within reach. Is it going to take some more work? You bet it is. But I think it’s within reach.”

“Now is the moment, following what happened with bin Laden, to put maximum pressure on them because I do believe that if we continue this effort we can really cripple al-Qaida as a major threat” to America, he said.

Al-Qaida’s attacks of Sept. 11 triggered the U.S.-led invasion of Afghanistan and the overthrow of the Taliban government that had sheltered bin Laden. But in the years since, the Taliban has reasserted itself and al-Qaida has managed to operate from havens in neighboring Pakistan.

Al-Qaida affiliates have emerged in Iraq, Yemen, Somalia, and elsewhere. That’s led many in the U.S. to argue for a shift from fighting the Taliban in Afghanistan to targeting al-Qaida leaders in Pakistan and other places.

Panetta, who planned to travel outside Kabul to visit U.S. troops Sunday, has endorsed President Barack Obama’s plan to begin drawing down U.S. troops this summer but keep a significant, though gradually shrinking, presence until the end of 2014.

At one point Saturday, Panetta told reporters that 70,000 troops would remain “through 2014.” His spokesman, Doug Wilson, later said Panetta meant to say that the 70,000 that will remain in September 2012 will be drawn down through 2014 on a schedule that has not yet been worked out.

On a lighter note, Panetta told reporters that he has gotten a feel for his new job. He compared it to his official aircraft, a towering military version of the Boeing 747.

“It’s big, it’s complicated, it’s filled with sophisticated technology, it’s bumpy, but in the end it’s the best in the world.”