Two improvised bombs exploded and an ensuing gun battle broke out while US forces were on patrol in Kunar province, near the town of Asadabad, 170km east of Kabul, US military spokesman Major Mark McCann said.
"One US soldier was killed and three others were wounded," he said, adding that it was unclear whether the soldier was killed by the blasts or the gunfight.
McCann was also unable to say who carried out the attack.
On Sunday, another US soldier died in the western Herat province during a raid on a compound.
The three soldiers who were wounded in Monday's attack were evacuated by helicopter to US military headquarters at Bagram Airfield and are in a stable condition, the US military said in a statement.
The US-led coalition still has more than 18,000 troops in Afghanistan, who are said to be in search of Taliban remnants.
The US military said its raid in the Shindand district in western Afghanistan on Sunday during which one of its troops died, was launched to arrest a former local commander Mullah Dost Muhammad.
"Coalition troops were led to a compound by a local Afghan who said Mullah Dost Mohammad, a known anti-coalition militant, was inside," McCann said.
US forces say they are in search
of Taliban remnants
He said troops entered a compound and fired at a suspect, who was allegedly shielding himself behind two civilians.
He said Muhammad was targeted for involvement in "activities counterproductive to security", but gave no further details.
"Mullah Dost was killed along with his wife, and two of their children were injured," local commander Akhtar Muhammad Husaini said.