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Sen. Dianne Feinstein, California Democrat and chairwoman of the Senate Select Committee on Intelligence, told Bloomberg News, “I don’t think there was a credible threat” that Sgt. Bergdahl was about to be killed.

Rep. Duncan Hunter, California Republican, asked Mr. Hagel in a letter last week to release the Pentagon assessment of the video.

“My understanding is that the document remains classified,” Mr. Hunter wrote. “I respectfully ask that you declassify the Bergdahl health assessment related to the December 2013 proof-of-life video.”

Brian Hale, spokesman for Director of National Intelligence James R. Clapper, said three “main factors” compelled the director to support the transfer.

“The first was evidence that Sgt. Bergdahl’s health was deteriorating. Our judgment was that every day he was a prisoner, his life was at risk, and in the video received in January, he did not look well,” Mr. Hale said.

“Second was the fact that, as we draw down our forces in Afghanistan, we will have fewer resources available to dedicate to his recovery. Lastly, that the DNI was satisfied with the assurances from the Qatari government that these five individuals will be closely monitored and subject to travel restrictions,” he said. “These factors, considered together with other information, led to an even greater sense of urgency in pursuing his recovery.”