Civilian casualties have caused public outrage, and Hamid Karzai, the Afghan president, has called on the foreign forces in his country to take greater care.
Nato said it regretted the latest loss of life.
The killing happened in Sangin district of Helmand province, one of the most dangerous areas of Afghanistan, with fighters opposed to Nato and the US-backed Afghan government active in the area.
On Thursday, a British army dog-handler and his explosives-sniffer dog were killed in the district after their patrol came under fire, the UK’s defence ministry said.
In the northeastern province of Takhar, Afghan police said they killed a Taliban commander on Friday after he attacked a police checkpoint with a group of fighters, the interior ministry said on Saturday.
Mullah Osman was the commander of anti-government operations in the country’s northeast, it said.
In the western province of Farah, Afghan soldiers said they killed five fighters and detained nine more during an operation that started on Thursday, the interior ministry said.
Nato coalition forces said they killed one fighter in the eastern province of Kapisa on Friday after he threatened the soldiers.