The U.S. military's Central Command Web site says the soldier died Wednesday as a result of injuries during operations in eastern Afghanistan's Paktika province.
On Thursday, the military said a coalition soldier had been slightly injured by a bomb while on patrol in the same region. It's not clear at this point whether those reports refer to the same incident, or two different incidents.
About 11,500 troops of the U.S.-led coalition are in Afghanistan hunting down remnants of the ousted Taliban regime and their allies, who are waging a low-level insurgency.
Thursday, Afghan officials said security forces captured six Taliban fighters in central Afghanistan, and in another incident, a U.S. helicopter attack left three people wounded.
The raids by U.S. and Afghan forces follow a step-up in combat with suspected Taliban forces, who are accused of attacking two police stations last Sunday. The first police station attack claimed 22 lives; the second attack involved several hundred assailants, who torched the building and abducted four police officers.
That was in Tarway, in Paktika, the eastern Afghan province where U.S. soldiers came under attack later in the week.
In central Afghanistan, Uruzgan provincial Gov. Jan Mohammed Khan says two of the guerrillas arrested Thursday were local commanders before a U.S.-led coalition toppled the Taliban in late 2001.
Khan says the troops also confiscated 40 rocket launchers, four AK-47 rifles and six grenades. He identified one of the commanders as Mullah Sharafuddin. The other leader was not named. Khan said nearly 200 Taliban fighters were hiding in the hills of Uruzgan district.
In a separate operation, Afghan officials say an American helicopter fired a rocket at a pickup truck carrying civilians in southeastern Afghanistan, injuring at least three people.
According to provincial police spokesman Khan Sayed, the truck was carrying six passengers when it came under fire late Wednesday at the Many Kandow Pass in Urgun district of Paktika province.
The U.S. military said that the helicopter fired on a truck that was "speeding aggressively toward coalition forces engaged in combat operations" near Gayan. But the military did not report any injuries or deaths.
The Taliban, ousted in late 2001, have been blamed for daring attacks on Afghan police in recent days, including in Paktika.
During their rule, the Taliban routinely traveled in pickup trucks. There have been reports from Afghanistan of coalition forces mistakenly firing on trucks, suspecting they were being operated by Taliban fugitives.
However, pickups are also regularly used by refugees returning across the border from Pakistan and by extended families who travel in large numbers.