The civilians, aged between 12 and 20, were killed while they were out hunting birds in the area of Saracha, a few kilometres from Jalalabad city, the capital of eastern Nangarhar province, provincial police spokesman Hazrat Hussain Mashreqiwal told AFP.
A NATO spokesman said he was aware of the airstrike but could not confirm any casualties.
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Their bodies were brought to the central hospital, he said.
Ahmad Zia Abdulzai, a provincial spokesman, confirmed the incident.
"Three of the civilians killed in the airstrike were school children, two were brothers," Mohammad Atif Shinwari a spokesman for the Nangarhar education department told AFP.
Civilian casualties in NATO operations have long been a source of friction between the Afghan government and US-led NATO troops, who are winding down operations as they prepare to withdraw by the end of next year.
Last month, a NATO airstrike killed at least 16 civilians including women and children in neighbouring Kunar province in eastern Afghanistan.
The airstrike hit a pickup truck and killed all on board, Afghan officials said. However, NATO denied that civilians died in the attack, saying the strike had killed militants.
Tens of thousands of civilians have been killed in Afghanistan since the Taliban launched their insurgency in 2001 after being ousted in a US-led invasion.
As NATO troops wind down operations and Afghan security forces take charge of security responsibility countrywide, violence has been on the increase.
More than 1,000 civilians were killed and around 2,000 others were injured in the first half of 2013, according to a UN report, a 23 per cent increase from the same period last year.
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