Asadullah Khalid, Kandahar's provincial governor, said Nato air strikes in the area had left nine civilians dead and wounded 11 others on Wednesday.
Nato said an operation was believed to have caused "several" civilian casualties.
The governor said the strike in Zhari district had hit three houses and that an unknown number of Taliban militants were also killed.
Nato's international security assistance force said it regretted any civilian casualties and that it made "every effort" to minimise the risk of collateral damage during operations.
In a separate attack on Wednesday, a rocket hit a house during a night time clash between suspected Taliban fighters and Nato and Afghan security forces in a southern Afghan village.
A resident said 13 villagers, including women and children, died.
Provincial police chief Ghulam Nabi Malakhel said at least one Taliban fighter was killed and three police wounded in Tajikai village in southern Helmand province before the rocket hit the house.
Also on Wednesday, six Taliban fighters have been killed in clashes between Taliban fighters and Afghan police in Helmand province, an Afghan governmental official told an Aljazeera correspondent.
However, a Taliban spokesman challenged the statement, saying only two Taliban fighters were killed in the incidents.
He said Taliban fighters killed 16 Afghan soldiers in the clashes.