A roadside bomb destroyed a Romanian tank near Kandahar airport on Tuesday where multinational forces in the region are based.
One of the soldiers was injured when he stepped on an explosive device as he went to help the other soldiers in the tank.
In Helmand province's remote Baghran Valley, American soldiers fought off a Taliban attack on a US position with machine-gun and mortar fire. Planes were called in to bomb Taliban fighters and "a few" were most likely killed, the US military said.
Local residents claimed two civilians had died in the US air raid.
Up to 60 Taliban insurgents launched the attack on US soldiers dug into a mountain ridge, firing a barrage of mortar rounds or rocket-propelled grenades at the soldiers, said company commander Captain Jared Wilson.
The attack followed a bombing raid on Monday by multinational force helicopters on a Taliban camp in the same area that killed five and wounded eight, the Helmand provincial governor's spokesman said.
The Taliban have stepped up their attacks in the south of the country. International forces say this is due to their own increased operations but some Afghan officials claim it is a sign of growing support for the Taliban and disillusionment with the government.
In advance of Nato's takeover in the south, US, British and Canadian troops have launched their biggest offensive in the region since 2001 to crush the insurgents and cut off supply routes.
The multinational force says Operation Mountain Thrust has killed more than 100 insurgents in recent days.
Police officers killed
In another incident, US forces shot dead three Afghan police officers who were on their way to disperse a group who had blocked a main road to protest about the shooting of two women by US soldiers, the provincial police chief said.
British, US and Canadian forces
have launched a big offensive
One of the two women later died in a US military hospital, Abdul Jalal Jalal said.
The women were wounded when US soldiers fired at homes in Wata Pur in the eastern Kunar province when a vehicle of the convoy they were in was hit by a roadside bomb.
"I had gone to attend the funeral of the woman," Jalal said. "Villagers and relatives of the woman were angry and went on the road to block it and I had to ask for police reinforcements. American soldiers were coming from opposite direction and fired at the police reinforcements."
US military officials have not commented on the incident.
Almost 1,000 people have died in violence in Afghanistan this year, including more than 40 foreign troops, most of them Americans. About 400 people were killed in May alone.