Troops opened fire against the demonstrators who were protesting against the attack, which President Hamid Karzais office said killed six civilians, including one woman.
NATO said no civilians had died in the attack in Laghman province, northeast of Kabul, saying its forces had killed seven militants and arrested four.
The acting head of Laghmans provincial council, Gulzar Sangarwal, said 13 civilians were killed in the pre-dawn raid in Armul village. A Reuters journalist in Armul saw the body of a woman and 12 men, including two teenagers, covered in shrouds.
Some 5,000 villagers marched to protest against the attack chanting slogans against the provincial governor, Karzai and foreign troops in Afghanistan, when Afghan troops opened fire.
The Reuters journalist said he had seen four demonstrators hit by bullets when the Afghan troops opened fire from a vehicle. Two died instantly, and two were taken to hospital, where residents said they died of their wounds.
Provincial authorities were not immediately available to comment about the shootings.
Civilian casualties caused by Western forces have stoked anger towards foreign troops, which NATO commander US General Stanley McChrystal says undermines his mission.
The NATO-led force issued a statement denying it had killed any civilians in the incident.
We are aware of civilian casualty allegations, however there are no operational reports to substantiate those claims of harming civilians, including women and children during this operation, said spokeswoman Navy Captain Jane Campbell.
The statement said the joint force came under hostile fire from multiple positions and returned fire in Armul village, in Mehtar Lam district.
The joint force searched the compound without further incident and recovered multiple AK-47 rifles.
Some Afghans are concerned that the influx of 30,000 more US troops ordered by US President Barack Obama last week will result in more attacks and higher civilian casualties.