The clash erupted in southern Uruzgan province on Friday when Afghan and coalition troops encountered militants while "conducting operations to improve security", a coalition statement said.
The six wounded soldiers were evacuated to a nearby medical treatment facility and are said to be in a stable condition.
Uruzgan is one of the provinces worst affected by an insurgency launched by the Taliban movement after it was overthrown in a US-led invasion weeks after the September 11, 2001 attacks blamed on Taliban ally, al-Qaeda.
About 25 other US soldiers have already died in Afghanistan this year, 13 of them in hostile action.
There has been a dramatic upsurge in fighting between security forces and Taliban rebels in the south of the country in the past week, with nearly 200 rebels and about 25 troops, police and civilians killed in days of fierce fighting.
The violence comes weeks before a NATO-led force is due to move into southern Afghanistan, taking over the bulk of operations from the coalition.
Taliban militant 'captured'
Meanwhile, Afghan officials are working to establish whether a seriously wounded one-legged militant captured after a gun battle was Taliban commander Mullah Dadullah.
Afghan forces on Friday said they had captured a man they described as a "very important Taliban" commander, but are yet to formally identify him.
Reports said he is being detained by international troops.
The governor of the southern province of Kandahar, Assadullah Khalid, confirmed the arrest of one of the Taliban's senior leaders but would not say who he was.
"We have captured a very important Taliban member but due to security reasons we cannot reveal his identity," Khalid told reporters on Friday.
The one-legged man was caught after a major battle that erupted in Kandahar's Panjwayi district on Wednesday and in which 100 rebels were killed, Khalid said.
General Rahmatullah Raufi, army commander for southern Afghanistan, told AFP the man could be Dadullah because he had similar features and was also missing a leg.
"During the fighting in Panjwayi district we have detained a person who is badly wounded and in a coma and he has got one leg," Raufi said.
"Now we are investigating to determine whether it is Dadullah or not. From the facial features of this person, it seems that he may be Dadullah but we are not sure."
The BBC reported that senior Afghan officials had said the captured man was Dadullah and he was being held by international troops.
The US-led coalition and NATO forces in the capital Kabul could not confirm the arrest to AFP.
Dadullah is one of the most influential leaders of Afghanistan's Taliban, having joined the movement at its birth in the early 1990s and going on to be a mastermind of the insurgency it is now waging.
He is close to fugitive Taliban leader Mullah Omar and has said he has links with the Al-Qaeda network.