MONTEREY, Calif. — Citing the myriad threats facing the United States, Defense Secretary Leon E. Panetta said Tuesday that one of the biggest challenges to U.S. national defense is the so-called “doomsday mechanism” that will trigger across-the-board budget cuts if Congress doesn’t make the decisions necessary to avert it.

Speaking to a standing-room-only audience at the Navy Postgraduate School’s King Hall in Monterey, Calif., Panetta told the students and faculty the across-the-board reductions could take another $500 billion to $600 billion from the defense budget over 10 years.

“It will be devastating to the defense budget,” resulting in a hollowed out force, weakened defenses and an inability to meet U.S. alliance obligations, he said. “It will break faith with troops and their families,” he said, adding that is a breach the United States must never allow.

“This is a moment when the leadership of our country is going to be tested” more than ever before, the secretary said.

Panetta said he firmly believes that the United States doesn’t have to choose between fiscal responsibility and national defense. “Both can be accomplished,” he said, “with smart, albeit difficult, and courageous decision making.”

“We have an opportunity to do this in a way that protects our national defense,” Panetta said, ensuring agile, deployable forces without breaking faith with service members and families.

“The opportunity is there” for the department to identify and institute its own cost reductions “in a way that makes us better,” he said, and preserves what he called the strongest military force in history.

Allowing that force and those capabilities to wane, isn’t an option, Panetta said. The country “is at a point in time where we can’t afford to weaken our national defense,” he said. “It’s important for us to maintain that strength for the future.”

Panetta said he spends every day looking at the myriad challenges facing the nation from many different directions.

Approaching the 10th anniversary of the 9/11 attacks, al Qaida’s leadership has been weakened, along with its ability to plan attacks against the United States, the secretary said. But al Qaida “is still a threat,” he said, recognizing the growing influence in places like Yemen, Somalia, and North Africa.

“We must never stop” pursuing terrorists until they have “no place to hide and … represent no threat to this country,” Panetta said. “We should never give up until we have defeated their intent to attack this country.”

As the United States draws down forces in Iraq and Afghanistan, Panetta said it must be done in a way that ensures stability and security, and builds on the many sacrifices of those who served there.