Afghan Taliban leader Mullah Mohammad Omar has issued a rare public statement hailing the exchange of five Guantanamo Bay detainees for a Taliban-held US soldier as a "big victory".
Sgt Bowe Bergdahl, 28, was handed to US forces in Afghanistan on Saturday.
The White House has defended the swap amid criticism from Republicans who said the deal was soft on terrorism.
Sgt Bergdahl's parents said their son's recovery would take a long time, in an emotional address on Sunday.
They said they had not yet spoken to the soldier, who is in a good condition and currently undergoing medical care at a US military hospital in Germany.
"Bowe's been gone for so long that it's going to be difficult to come back," his father, Robert Bergdahl, told journalists at a news briefing in Idaho, the family's home state.
Jani and Bob Bergdahl spoke of their love and pride for their son, Sgt Bowe Bergdahl, and said he would need time to ''decompress''
"It's like a diver going deep on a dive and [having] to stage back up through decompression to get the nitrogen bubbles out of his system. If he comes up too fast, it could kill him."
The parents earlier revealed that Sgt Bergdahl had trouble speaking English. He was the only US soldier being held by the Taliban in Afghanistan.
'Breach of law'
Earlier on Sunday, Mullah Omar, who has made no public appearances or speeches since fleeing Afghanistan in 2001 when US-led forces toppled the Taliban after the 9/11 attacks in the US, said: "I extend my heartfelt congratulations to the entire Afghan Muslim nation."
The Afghan government, which was not informed of the deal until after the exchange had taken place, has condemned it as a "breach of international law".
"We are strongly opposed to it," it said in a statement, adding: "We want Qatar and the US government to let the men go free."
The five senior Afghan detainees are thought to be the most senior Afghans held at the US detention facility in Cuba, having been captured during America's military campaign in 2001.