The clash occurred in Paktika province after the insurgents attacked a patrol of U.S.-led coalition and Afghan forces, a military statement said. The militants fled after the fighting and American forces deployed attack aircraft in pursuit.
"Our patrols of coalition and Afghan forces are relentless in the pursuit of the enemy," Army Brig. Gen. Jack Sterling, deputy commanding general of Combined Joint Task Force-76, was quoted as saying in the statement. "We are deeply saddened by the loss of our soldier and will honor him by continuing to take the fight to the enemy."
Two of the wounded U.S. soldiers were taken to a nearby base for treatment while the third was treated and returned to duty, it said.
Fighting in Paktika has killed five U.S. troops in the past week. The province is next to the Pakistani border and militants based in tribal regions on the other side of the mountainous frontier often cross into Afghanistan to launch attacks, Afghan officials say.
Seventeen suspected Taliban militants were reported captured in the border area Monday.
"The enemy may still be powerful at times, but not nearly as powerful as the combined efforts of Afghan and coalition forces when fighting alongside each other," U.S. military spokesman Lt. Col. Jerry O'Hara told The Associated Press by telephone.
The death brought to 149 the number of U.S. military personnel killed in and around Afghanistan since the Taliban were driven from power in 2001.
Even though U.S. military commanders express optimism about progress toward making Afghanistan secure, there has been a sharp rise in bombings, shootings and other violence since winter's snow melted in mountain passes used by insurgents.
Security forces have hit back hard, killing more than 200 suspected militants since March, U.S. and Afghan officials say.