"An improvised explosive device was detonated ... in the province of Oruzgan, killing one Afghan National Army soldier," US military spokesman Major Mark McCann said on Saturday.
Twelve other soldiers were wounded in the incident, he added.
On Friday one US unit was attacked in the same province by three armed men.
"As a result, one militant was wounded and later died of his wounds," the spokesman said.
Fighters from the Taliban, whose government was toppled by a US-led operation in late 2001, regularly attack foreign and local troops, mainly in the south and southeast of the country.
More than 800 people have died mainly in Taliban-linked violence last year despite the presence of 18,000 US-led troops in the country to hunt down the fighters.
The US-backed government of President Hamid Karzai is working on an amnesty scheme with the Taliban to help calm the war-shattered country as it struggles to rebuild itself after decades of conflict.
On Thursday, Afghan regional commander Abd al-Rashid Dustum narrowly escaped assassination when a bomber blew himself up, injuring at least 21 people in the Dustum's northern stronghold of Sheberghan.
The Taliban claimed responsibility for the attack.