The children and a local police officer died when a suicide bomber riding a motorbike exploded his vest in front of a school in Samkani district, in eastern Afghanistan's province of Paktiya, police chief Zamlai Oriyakhel said.
The bomber was believed to have targeted a US-led military convoy. The NATO-led forces confirmed that two of its troops had also been killed in the attack. The attack had also left 20 civilians and one local police officer injured.
In a separate incident in Laghman province, seven civilians – five of them women - were killed while on their way to collect firewood when a roadside bomb hit a truck, the Afghan Ministry of Interior said.
The ministry blamed the Taliban, who frequently deploy roadside bombs to target Afghan and NATO-led troops.
The Taliban were not immediately available for comment.
In the southern province of Kandahar, an Afghan man working for a de-mining organization was also killed in a NATO airstrike.
The man, identified as Mohammad Khan, had been working in the radio operations department of the local MCPA de-mining organization.