US officials said the soldier died of his wounds as a result of fighting near Shkin.
"The soldiers were engaged in a combat manoeuvre against anti-coalition soldiers," Colonel Rodney Davis said.
"Coalition forces killed two enemy personnel with small arms fire."
Shkin base in Paktika province, about 280 kilometres south of Kabul, is regularly targeted by suspected Taliban fighters, alleged to be regrouping over the border in Pakistan.
On Monday, Aljazeera aired a tape of a Taliban spokesperson Mullah Hidayat Allah Akhhond urging resistance fighters in Afghanistan, Iraq, Palestine, and Chechnya to continue their stuggle for freedom.
The senior Taliban commander went on to urge Afghans to resist attempts to drag them into ethnic conflict and criticised US-backed Afghan president Hamid Karzai.
Al-Zawahiri blasted Pakistan's
It was the first public broadcast by any representative of the Taliban, in contrast with the relatively frequent al-Qaida tapes.
A day earlier, Aljazeera aired an audiotape of Usama bin Ladin's spokesperson Ayman al-Zawahiri, calling for the overthrow of Pakistani President Pervez Musharraf.
He blamed Musharraf for helping the US topple the Taliban and has claimed that Musharraf is preparing to announce Pakistan's recognition of Israel - considered an insult in the Muslim world.
In his tirade of Musharraf, al-Zawahiri added that Pakistan was in the process of sending troops to Iraq.
"Musharraf ... is seeking to send Pakistani forces to Iraq so that they, rather than American soldiers, are killed and so that they kill Muslims in Iraq and enable America to control Muslim lands."
He also warned Pakistani army officers and soldiers the president would "hand you over to the Hindus and flee to enjoy his secret [bank] accounts" if India attacked their country.