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Asked about reports that Sgt. Bergdahl had deserted his unit in Afghanistan five years ago, Mr. Carney said the Defense Department will evaluate “all of the circumstances” of his capture by the Taliban. But he didn’t repeat the assessment of White House national security adviser Susan E. Rice, who said Sgt. Bergdahl “served the United States with honor and distinction.”

State Department spokeswoman Jen Psaki twice declined to call Sgt. Bergdahl a deserter.

“We would characterize him as a member of the military who was detained while in combat,” she said.

Former Bush administration official John Bolton said by trading for a terrorist group’s hostage, “we are invariably putting a price on the heads of other Americans.”

“Exchanging Bergdahl for five terrorists is functionally no different,” Mr. Bolton wrote in the New York Post. “The Reagan administration was wrong in Iran-Contra to deal for hostages, and it almost cost Reagan his presidency. It is equally wrong today.”