One attacker was killed in the firefight outside an air base for US-led foreign fighters near Khost city, they said.
As a US jet roared overhead, US and Afghan ground troops searched for the attackers, according to residents living nearby.
"Right now two helicopter gunships and a jet plane are flying over a village where the attackers are said to have fled," Kheyal Baz Khan, the top provincial military official, said.
"We know one of the attackers was killed after hurling hand grenades on the convoy and one American soldier was wounded," he told Reuters news agency from Khost.
The US military in Kabul said it had no immediate information about the incident.
'Heart of fighting'
Khost is at the heart of a violent insurgency led by the ousted Taliban and their al-Qaida allies near the rugged Pakistani border.
Friday's ambush follows a spate of intensifying raids in the past two weeks by suspected remnants of the Taliban, which US-led forces drove from power in late 2001.
US forces face regular attacks
At least seven government soldiers were killed in two separate raids by Taliban fighters in the southern provinces of Helmand and Kandahar on Thursday night, officials said.
The soldiers were killed late on Thursday in Panjwai district while tracking remnants of the Taliban.
Recent attacks in Kandahar, a former Taliban stronghold, include the killings of two Afghan aid workers on Monday. No further details of Thursday's clash were immediately available.
The killings follow the arrest of 18 Taliban members suspected of killing the aid workers.
The United Nations called for urgent security measures in Kandahar, where it has been forced to reduce activities such as voter registration.
The United States, which leads a force of 15,500 foreign troops in Afghanistan, has said the recent attacks appear aimed at destabilising the country before September elections, which have already been delayed from June partly due to violence.
The Taliban has declared war against US-backed President Hamid Karzai's government, foreign troops and aid workers in the country.
Nearly 700 people have died, mostly in the south and east, since August, the bloodiest month since the Taliban's fall.
More than 80 American soldiers have been killed and dozens wounded in combat operations in Afghanistan since the Taliban fell, according to estimates.