The fighting started on Friday when Afghan and coalition troops encountered local fighters while on a security mission, military sources said.
Aljazeera quoted Muhamed Hanif, a Taliban spokesman in Afghanistan, as saying fighters attacked a convoy of US troops and burned four vehicles in the fighting. He said five fighters were also killed.
The six wounded soldiers were evacuated to a nearby medical treatment facility and were in a stable condition.
About 25 US soldiers have died in Afghanistan this year, including 10 who were killed earlier this month when their helicopter crashed during an operation in the eastern Kunan province.
Fighting has also increased in recent months between coalition forces and fighters loyal to the country's former Taliban government.
Up to 100 people died in fierce clashes between Taliban forces and Afghan police last week in the Helmand province and the southern city of Kandahar.
Meanwhile, a man claiming to be Mullah Dadullah, a Taliban commander, called Reuters news agency late on Friday to deny recent reports that he had been captured.
"I am Mullah Dadullah. The reports about my arrest are not only false but a pack of blatant lies," he is quoted as saying.
Several news reports earlier on Friday said that Dadullah, along with two other senior Taliban commanders, had been captured in the country, but these were not confirmed by Afghan officials.