A US soldier was killed during the firefight, the alliance confirmed.
Taliban militants are most active in the country's southern and eastern regions, which border Pakistan. The Taliban, who lost power in Afghanistan in a US-led military invasion in late 2001, are widely believed to have moved their command bases into the lawless Pakistani tribal areas.
The US government sent more than 20,000 additional troops to Afghanistan this year to help provide security for last week's elections and to quell the Taliban-led insurgency.
The latest fighting occurred as Afghanistan awaits election results. President Hamid Karzai is leading in the recently released partial results, but his challengers have accused the incumbent of rigging the vote.
The Independent Election Commission said no further partial results will be available before the weekend.
The final results of the vote are expected around Sep 17.
Allegations of fraud and irregularities could undermine US President Barack Obama's hopes for a functional Afghan government to tackle the insurgency in the war-shattered country.