The U.S. military say the clash occurred as Afghan and U.S. troops were conducting a joint patrol on 15 December.
It added that one militant was also killed, while one U.S. soldier and an Afghan soldier were wounded.
On 12 December, four coalition soldiers were wounded when their vehicle struck a mine in the same province.
RFE/RL Afghanistan Report
SUBSCRIBE For regular news and analysis on Afghanistan by e-mail, subscribe to "RFE/RL Afghanistan Report."