A homemade bomb also exploded on Friday in a busy market in the southern city of Kandahar, wounding four people including a woman and child.
Aljazeera's correspondent in Afghanistan reported that five Afghans were killed and three others wounded in clashes between Taliban fighters and government forces in the provinces of Zabul, Helmend and Kandahar.
The security chief of Zabul province said two Taliban fighters had ambushed an Indian company, killing a worker and wounding another.
In the directorate of Arghndab in the province of Kandahar, three Taliban elements were also reported killed and two policemen were wounded, the reporter added.
The Taliban announced it had killed four people in the province of Helmend, claiming they were spying for US forces.
Taliban leader killed
A US military statement said Taliban commander Qari Amadullah was killed near Wazikhwa in eastern Afghanistan on Tuesday.
"Amadullah was believed to have commanded up to 50 Taliban fighters in the region and was thought to be in possession of a number of weapon systems to include rockets and rocket-propelled grenades," it said.
Taliban spokesman Abdul Latif Hakimi confirmed the incident.
Amadullah was killed during a clash with Afghan soldiers and US paratroopers in which five other fighters died and three US servicemen were wounded.
"Killing this individual will significantly disrupt Taliban operations in the region," said US Brigadier-General James Champion.
The US military also said one American soldier had died in a training accident involving explosives near Tarin Kot in the southern province of Kandahar.
The death brought to six the number of US military personnel killed this month in Afghanistan, three of whom died in combat.
Forty-one US servicemen died in
combat in Afghanistan this year
Forty-one US servicemen have died in combat in Afghanistan this year, the bloodiest period for Washington since it sent troops to help overthrow the Taliban in the aftermath of the 11 September attacks on the United States in 2001.
Hundreds of Afghan soldiers, police and civilians have also been killed in fighting led by remnants of the Taliban in the run-up to 18 September parliamentary polls, the next big step in Afghanistan's difficult path to stability.
This week alone, Afghan and US officials have reported the deaths of more than 40 fighters.