The United States is “within reach” of defeating al-Qaeda and is targeting 10 to 20 leaders who are key to the terrorist network’s survival, Defense Secretary Leon Panetta said on Saturday during his first trip to Afghanistan since taking charge at the Pentagon.

Panetta, who led the CIA until June and oversaw the raid that killed Osama bin Laden, strongly endorsed the Obama administration’s increasingly aggressive campaign to hunt down al-Qaeda leaders in Pakistan, Yemen and Somalia. He hinted of more to come, saying he would redouble efforts by the military and the spy agency to work together on counterterrorism missions outside the traditional war zones of Afghanistan and Iraq.

“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 that we can really cripple al-Qaeda as a threat to this country,” he told reporters on his plane en route to Afghanistan.

“I’m convinced,” he added, “that we’re within reach of strategically defeating al-Qaeda.”

Panetta’s remarks were his first public comments since he became defense secretary on July 1, as well as perhaps the most optimistic assessment by the Obama administration regarding the long-running conflict with al-Qaeda.

Although the CIA and the U.S. military have assembled lists of al-Qaeda leaders targeted for assassination or capture ever since the Sept. 11, 2001, attacks, Panetta argued that the longtime strategy of trying to defeat the network by focusing largely on its senior ranks — an approach that analysts refer to as “decapitation” — was finally paying dividends.

His statements about a fading al-Qaeda were echoed shortly after his arrival in Kabul on Saturday by Gen. David Petraeus, the outgoing commander of U.S. and NATO forces in Afghanistan. Petraeus said that the counterterrorism campaign in the remote tribal areas of Pakistan, near the Afghan border, had done “enormous damage” to al-Qaeda beyond the killing of bin Laden.

“That has very significantly disrupted their efforts,” Petraeus added, “and it does hold the prospect of really a strategic defeat — if you will, a strategic dismantling of al-Qaeda.” Petraeus is retiring from the Army this summer and is scheduled to take over Panetta’s job as director of the CIA in September.

‘Al-Qaeda’s obituary’

Bin Laden’s network formally declared war against the United States in 1996 and has outlived many other predictions of its demise. Over the years, the group has demonstrated the discipline and ability to replace dozens of operational commanders responsible for plotting attacks.

“Al-Qaeda’s obituary has been written countless times over the past decade,” said Bruce Hoffman, a terrorism expert and professor of security studies at Georgetown University. “Each iteration has proved to be ephemeral, as the moment has continually shown itself to have a deeper bench than we imagine.”

“While it is certainly true that al-Qaeda’s leadership has been significantly eroded over the past two years, there is no empirical evidence that either the appeal of its message or the flow of its recruits has actually diminished,” Hoffman added.

U.S. officials have said they recovered a huge amount of computerized data about al-Qaeda’s internal communications when they located and killed bin Laden at a compound in Pakistan in May. So far, however, hopes that the information would enable the CIA to quickly roll up the rest of the network’s leadership have faded.

A top operational commander, Ilyas Kashmiri, was reported killed by a U.S. drone strike in Pakistan last month. But al-Qaeda has demonstrated a proven ability over the years to replace field commanders like him.

Replacing bin Laden will present al-Qaeda with a much tougher challenge. The Saudi native helped found al-Qaeda more than two decades ago, and the network required most of its followers to swear their personal loyalty to him. His longtime deputy and chosen successor, Ayman al-Zawahiri, an Egyptian surgeon, is considered a divisive figure within the movement.

Panetta said U.S. intelligence officials believe that Zawahiri is hiding in Pakistan’s remote tribal areas near the Afghan border — unlike bin Laden, who spent years holed up in a large compound in Abbottabad, a military garrison town not far from the capital, Islamabad.

For years, Pakistani officials had adamantly denied that bin Laden could have been in their country, fueling U.S. suspicions that Pakistan was, at a minimum, not interested in helping to find him. As a result, the Obama administration deliberately kept the bin Laden raid a secret from the Pakistanis, fearing they might tip him off in advance.

Since then, Panetta said he has personally urged Pakistani intelligence officials to work jointly with the United States to find Zawahiri.

“He’s one of those that we’d love to see the Pakistanis target, along with our capabilities as well,” Panetta said.

The threat from Yemen

While al-Qaeda’s haven in Pakistan has received renewed attention since bin Laden’s death, Panetta repeated the CIA’s assessment that the network’s affiliate in Yemen has become a more immediate threat to the United States.

“There’s no question that if you look at what constitutes the biggest threat in terms of attacks on the United States right now, a lot of that comes from Yemen,” Panetta said.

Panetta’s trip to Afghanistan comes shortly after President Obama’s announcement that he will withdraw 33,000 U.S. troops from the country by September 2012, leaving a total of 68,000 by that date.

After meeting Saturday evening with Afghan President Hamid Karzai, Panetta made his first gaffe since becoming defense secretary when he told reporters — twice — that 70,000 U.S. troops would remain in Afghanistan through the end of 2014, effectively stretching Obama’s timetable by two years. He stood by his statements even when asked pointedly if that’s what he really meant.

Obama has said the United States will continue to withdraw troops between 2012 and 2014, though he has not specified how many will leave during that period. Panetta’s spokesman, Douglas Wilson, later said that the new Pentagon chief had misspoken and that there was “no daylight” between his stance and Obama’s on troop withdrawals.