Mohammed Arish, a government administrator in Surkh Rod, said a father and his four sons and four members of another family were among the dead.
"They are farmers. They are innocent. They are not insurgents or militants," Arish told The Associated Press by phone.
Arish said the protesters had tried to march toward the provincial capital of Jalalabad before being turned back by police.
The Nangahar governor's office said at least three people were injured during a clash with police.
'Taliban firefight'
A Nato spokesman confirmed foreign and Afghan forces had conducted some operations in the area but said he was not aware of any civilian deaths and the alliance was checking the incident.
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"Nato and Isaf said they were targeting Taliban sub-commanders and some fighters which their intelligence said were hiding in a compound outside a village"
Hoda Abdel Hamid, Al Jazeera correspondent
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Colonel Wayne Shanks said eight Taliban fighters were killed in a firefight, adding that fighters fired rocket-propelled grenades at Nato forces.
Two other people were captured during the operation, and weapons and communications gear were confiscated at the targeted compound, Shanks said.
Al Jazeera's Hoda Abdel Hamid reporting from Kabul said international forces and Afghan troops were flown to the area by helicopters overnight and carried out the raid.
"According to a Nato and Isaf [International Security Assistance Force] statement they were targeting Taliban sub-commanders and some fighters which their intelligence said were hiding in a compound outside a village.
"But the villagers said none of those killed had anything to do with the Taliban, that all of them were innocent civilians and members of two different families."
Sensitive issue
Civilian deaths at the hands of US and Nato forces are a highly sensitive issue in Afghanistan.
Last year public outrage over such deaths led General Stanley McChrystal, the Nato commander, to tighten the rules on combat if civilians are at risk.
He also ordered allied forces to avoid night raids when possible and bring Afghan troops with them if they do enter homes after dark.
Hamid Karzai, the Afghan president, discussed the issue in meetings with US officials in Washington this week. He has previously sought a complete ban on night raids.
"Civilian casualties is not only a political problem ... I don't want civilian casualties," Barack Obama, the US president, said on Wednesday after meeting Karzai.
"I take no pleasure in reading a report where there is a civilian casualty. That's not why I am president, that's not why I am commander in chief."
Last year was the deadliest for Afghan civilians since the war started in 2001, according to the United Nations.
Afghan officials say about 170 Afghan civilians were killed between the months of March and April this year alone, an increase of 33 per cent compared to the same period last year.
