Another Seal was rescued on Saturday and the fate of a fourth was unknown.
The official who confirmed the recovery of the two bodies spoke on Monday on condition of anonymity.
The team was reported missing last Tuesday. A rescue effort the same day ended in tragedy when the transport helicopter seeking to extract the team was shot down, killing 16 troops on board.
The serviceman rescued on Saturday had taken shelter in an Afghan village elder's home in the province before American forces were notified of his location and picked him up, Kunar provincial governor Asadullah Wafa said.
Claim of capture
A purported Taliban spokesman, Mullah Latif Hakimi, said last week that fighters had captured one team member. He said the "high-ranking American" was caught in the area where the helicopter went down.
A purported Taliban spokesman
says it captured a US Navy Seal
Hakimi, who also said fighters shot down the helicopter, often calls news organisations to take responsibility for attacks, and the information frequently proves exaggerated or untrue. His exact tie to the Taliban leadership is unclear.
US officials said they had no evidence indicating any service members had been captured.
The Navy Seal rescued from Kunar province was being evaluated on Monday, officials said. He was in stable condition and receiving medical treatment at the main US base at Bagram. No other information was released.
In a separate development, a joint United Nations-Afghan government electoral commission condemned Sunday's killing of a senior pro-government cleric, Mohammed Nabi Misbah, in the southern city of Kandahar.
Misbah had been working for the commission ahead of elections, said Bronwyn Curran, an organisation spokeswoman. Police have blamed the Taliban for the attack.
US air strike
Meanwhile, Kunar's provincial governor Wafa said on Tuesday that a US air strike on Friday had killed 17 people.
An initial US warplane bombing destroyed a house. As villagers gathered to look at the damage, a second bomb was dropped on the same target, killing 17 people, Kunar said.
The US military said the attack was carried out "with precision-guided munitions that resulted in the deaths of an unknown number of enemy terrorists and non-combatants".
The US says the attack in Kunar
"The targeted compound was a known operating base for terrorist attacks in Kunar province as well as a base for a medium-level terrorist leader," it said. "Battle damage assessment is currently ongoing."
Wafa said on Monday it was unclear who was killed in the initial attack in the tiny village of Chechal. "Maybe some militants were killed, but I don't know," he said.