Earlier, an Afghan military official said Afghan forces killed four suspected guerrillas on Thursday.
More than 350 people, including civilians, Afghan troops, rebels, aid workers and at least 11 US-led soldiers or CIA operatives, have been killed in attacks in Afghanistan since early August.
The violence is the worst since US-led forces overthrew the Taliban regime two years ago on Thursday.
US Central Command said in a statement the special operations soldier died on Friday near Asadabad, in eastern Afghanistan. It gave no more details.
Afghan and US forces are scouring mountains and villages in that part of the country as part of a new operation against fighters called “Mountain Resolve”, villagers reported.
At least four Afghans were killed and three hurt on Wednesday when their car was blown up by a remote-controlled bomb apparently intended for a US vehicle close to a US base in the area.
On Thursday night, in Shaplung in the province of Khost to the southeast, Afghan forces killed four suspected guerillas when they tried to overrun a government base near the border with Pakistan, an official said.
The clash lasted for an hour before the attackers retreated to Pakistan, said Kheyal Baaz Khan, a top provincial military official.
The violence is the worst since US-led forces overthrew the Taliban regime two years ago.
“Four Taliban or al-Qaida members were killed in their abortive attack in which no government soldier was harmed,” he told Reuters.
He did not have further details of the clash in remote Shaplung. Afghan officials say Taliban and al-Qaida guerrillas use Pakistani territory to orchestrate raids on Afghan soldiers, US-led forces and aid workers.
About 11,500 US-led troops are hunting remnants of the Taliban and al-Qaida as well as followers of Gulbuddin Hekmatyar, former prime minister and renegade warlord who has declared a jihad, or holy war, against foreign troops on Afghan soil.