The comments came hours after President Barack Obama defended the swap, citing a “sacred” obligation not to leave American soldiers behind even as the nation's top military officer said the circumstances around Bergdahl's capture would be scrutinized.
Obama, speaking to reporters in Poland on Tuesday, expressed confidence that the United States could still go after the militants if they pose a future threat to national security.
"We will be keeping eyes on them,” the president said. “Is there the possibility of some of them trying to return to activities that are detrimental to us? Absolutely," he said.
"We have confidence that we will be in a position to go after them if in fact they are engaging in activities that threaten our defenses."
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The five men would be banned from playing any political role in the Taliban or speaking to media, the gulf diplomatic source said.
However, the former detainees are being housed in a private compound similar to typical facilities for expatriate workers.
"There was never any discussion to move them from one jail to another jail,” the source told NBC News. “It is not where they go in [the capital] Doha that matters, it's what they do.”
Asked about reports the detainees will have freedom of movement in Qatar, Pentagon Press Secretary Rear Admiral John Kirby said that, "Secretary Hagel determined that this transfer was in the national interest. He is comfortable with the security assurances we received from the Qatari government."
What happens after their one-year travel ban expires was not immediately clear.
The five, who had been held at Guantanamo Bay since 2002, arrived in Qatar on Sunday where U.S. security personnel handed them over to Qatari authorities in the Al Udeid area west of Doha, site of a U.S. military base.
The deal has been blasted by Republicans, including Sen. John McCain of Arizona, who described the former detainees as “hardened” terrorists, the kind of militants who, upon release, are likely to return to the fight. They “have the blood of Americans and countless Afghans on their hands,” he said.
“In effect, we released the ‘Taliban Dream Team,’” Sen. Lindsey Graham, R-S.C., wrote in a letter to the chairman of the Senate Committee on Armed Services. “The United States is less safe because of these actions.”
— Ayman Mohyeldin
NBC News Jim Miklaszewski and Courtney Kube and Reuters contributed to this report.