The coalition said its troops were attacked Friday while searching compounds in the Shinwar district of Nangarhar province.
"Several militants were killed" and nine insurgents were arrested, the coalition said in a statement Saturday.
The coalition said the operation was targeting a "foreign fighter network" and that militants in the area had recently attacked coalition forces. The troops destroyed several automatic rifles, grenades and ammunition discovered in the compounds. Interior Ministry spokesman Zemeri Bashary said the government is investigating the villagers' claims.
"The coalition claimed they were fired upon from a house and the enemy were gathered there, but the villagers claim those people who were killed were innocent civilians," said Mohammad Hashem Ghamsharik, spokesman for the Nangarhar governor.
The head of the Nangarhar provincial council, Fazel Hadi Muslimyar, said police opened fire on the protesters, killing one and wounding three. Police refused to comment.
The Afghan government has pleaded with coalition forces to coordinate more closely to avoid civilian casualties, but foreign troops says insurgents hide in villages, using civilians as human shields.
More than 1,200 people, mostly militants, have died so far this year in insurgency-related violence in Afghanistan, according to an Associated Press count.
Separately, in central Kapisa province, a coalition vehicle hit a roadside bomb on Friday in Tag Ab valley, killing one service member, the coalition said. It did not give details.