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The president’s adviser said that in discussing counter terror operations, Mr. Obama “has encouraged us to be even more aggressive, even more proactive, and even more innovative” than they have been proposing.

But Mr. Brennan lamented “inflammatory rhetoric, hyperbole, and intellectual narrowness” surrounding the national security debate and said Mr. Obama has views that are “nuanced, not simplistic; practical, not ideological.”

Juan Zarate, a former deputy national security adviser for counterterrorism to President George W. Bush, was in the audience and dismissed Mr. Brennan’s speech as cosmetic in nature.

The focus on terminology, he said, is “almost a nonissue.”

“It’s a straw man. The question is, how do you deal with the policy?” Mr. Zarate said.

Mr. Zarate also discounted Mr. Brennan’s insistence that the Obama administration is not continuing Bush-era policies. Mr. Brennan gave credit for al Qaeda’s “damaged” capabilities only to front line military and intelligence personnel, while bashing the Bush administration for approving policies that green-lighted interrogation techniques such as waterboarding.

Mr. Brennan also said that under the Bush administration counterterrorism became too much of an emphasis and was “defining” and “distorting” U.S. foreign and national security policy.

But critics on the left and the right have pointed out that the Obama administration has continued such Bush-era policies as extroardinary rendition, drone attacks in Pakistan, an international and domestic surveillance program that remains cloaked in mystery, and the war in Afghanistan, where Mr. Obama has increased the number of U.S. troops and the military continues to house enemy combatants at Bagram Air Base.

In addition, the White House is still considering the practice of indefinite detention of terrorist suspects.

“A challenge for John and the administration is to preserve the perception of a new approach while still continuing with counterterrorism strategies that have proven effective,” said Mr. Zarate.