Hagel was referring in part to the threat from Bergdahl's captors when he said Sunday that "there was a question about his safety," administration officials told the senators.
In the briefing, both Republican and Democratic senators complained that not even the chairman and ranking member of the Intelligence Committee, who are trusted with some of the nation's most sensitive secrets, were notified of the agreement, said three congressional officials who were in the briefing. They spoke only on condition of anonymity because they were not authorized to discuss the matter by name.
Sen. Angus King, an independent from Maine, told The Associated Press in an email: "We were briefed that if these discussions had leaked out, there was a reasonable chance Bowe Bergdahl may have been killed. And that was one of the pieces of information that gave some credence as to why it had to be kept quiet."
Taliban fighters freed Bergdahl on Saturday and turned him over to a U.S. special operations team in eastern Afghanistan. Under the deal, five Taliban militants were released from Guantanamo and flown to Qatar, where they are to remain for a year under a travel ban and other restrictions that have not been spelled out in public.
A Taliban spokesman, Zabihullah Mujahid, told The Associated Press on Friday that Bergdahl was treated well.
Bergdahl was held under "good conditions," and was given fresh fruit and any other foods he requested. "You can ask him in America about his life (in captivity). He will not complain," Mujahid said in a telephone interview. He said the soldier enjoyed playing soccer as well as reading, including English-language books about Islam.
A senior administration official, who wasn't authorized to discuss the matter by name and spoke on condition of anonymity, said that "senators were told, separate and apart from Sergeant Bergdahl's apparent deterioration in health, that we had both specific and general indications that Sergeant Bergdahl 's recovery — and potentially his life — could be jeopardized if the detainee exchange proceedings were disclosed or derailed."
Associated Press writers Robert Burns, Lara Jakes, Bradley Klapper, Nedra Pickler and Donna Cassata in Washington and Lolita C. Baldor in Paris and Amir Shah in Kabul, Afghanistan, contributed to this report.