Two Republican lawmakers, Rep. Howard "Buck" McKeon of California and Sen. James Inhofe of Oklahoma, said Obama violated U.S. law when he approved an exchange involving prisoners at Guantanamo without notifying Congress 30 days in advance.
In response, the White House said that officials considered what they called "unique and exigent circumstances" and decided to go ahead with the transfer in spite of the legal requirement.
On Sunday, Susan Rice, the national security adviser said on ABC's "This Week" there had been extensive consultations with Congress in the past about getting Bergdahl back and that lawmakers knew the idea of trading detainees was on the table.
Hagel, who was traveling to Afghanistan to meet with U.S. troops, said notice of Saturday's action was not relayed to Congress because of its urgency. He said intelligence indicated that Bergdahl's "health was deteriorating."
At Bagram Air Field, Hagel thanked the special operations forces that participated in the rescue. Gen. Joseph Dunford said there was a sense of excitement in the headquarters as the news spread.
"You almost got choked up," he said. "It was pretty extraordinary. It has been almost five years and he is home."
Bergdahl's parents, Bob and Jani, led a tireless campaign to keep their son's story in the public eye. They were expected to hold a news conference Sunday in their hometown of Hailey, Idaho, where residents were planning a homecoming celebration for the soldier.
Bergdahl, in good condition and able to walk, was handed over to U.S. special operations forces by the Taliban in an area of eastern Afghanistan, near the Pakistani border, U.S. officials said. In a statement on its website, the Taliban put the location on the outskirts of Khost province.
The government of Qatar served as the go-between in the negotiations. Qatar is taking custody of the five Afghan detainees who were held at Guantanamo.
In weighing the swap, U.S. officials decided that it could help further the effort to reach reconciliation with the Taliban, something the U.S. sees as key to reaching a level of security in Afghanistan. But they acknowledged that there was a risk of emboldening other insurgent groups who might grab U.S. troops or citizens in an effort the secure the release of others prisoners.
Several dozen U.S. special operations forces, backed by multiple helicopters and surveillance aircraft, were involved in securing Bergdahl's transfer from about 18 Taliban members.
Bergdahl is believed to have been held by the Haqqani network since June 30, 2009. Haqqani operates in the Afghanistan-Pakistan border region and claims allegiance to the Afghan Taliban but operates with some degree of autonomy.
The U.S. believes Bergdahl was held for the bulk of his captivity in Pakistan, but officials said it was not clear when he was transported to eastern Afghanistan.
Officials said Bergdahl was taken to Bagram Air Field for medical evaluations, then transferred to Landstuhl Regional Medical Center, a military facility in Germany, before he's returned to the U.S. An official said Bergdhal was tentatively scheduled to go to the San Antonio Military Medical Center where he would be reunited with his family.
Bergdahl's parents had been in Washington on a previously planned visit when Obama called Saturday with news of their son's release.