Also in the south, 13 insurgents were killed by a missile that international forces fired from an unmanned drone, NATO said.
A protest of about 2,000 people in Helmand province's Garmsir district turned violent as demonstrators fought with security forces, leaving six civilians dead, according to the top official in the province, Abdullah Barak. Provincial spokesman Daoud Ahmadi confirmed six dead but did not say if they were civilians.
NATO said only one person was killed during the protest — an insurgent sniper who allegedly shot at an Afghan official and was killed by NATO troops.
A NATO spokesman denied that the foreign troops desecrated any copies of Islam's holy book in Sunday's operation with Afghan forces in Garmsir. Lt. Nico Melendez said no shots were fired, and no property was damaged.
"We take such allegations very seriously and would support a combined investigation with local Afghan authorities," he said.
Afghanistan is a Muslim nation where blasphemy of Muhammad and the Koran is considered a serious crime that is punishable by death.
Similar allegations that U.S. troops desecrated the Koran during an operation in October in Wardak province also sparked protests. U.S. and Afghan authorities denied the allegation, insisting that the Taliban are spreading the rumor to stir up public anger.
Tensions have intensified in southern Afghanistan as U.S. and other foreign troops step up their efforts to rout the Taliban.
Coalition troops saw a group of insurgents near a safe house preparing ammunition as well as insurgent mortar teams moving equipment in the Naw Zad area of Helmand province, NATO said. The international force launched one missile, killing the 13 militants.
On Monday, another missile fired from an unmanned aircraft killed three insurgents farther south in the Nad Ali district of Helmand, according to NATO.
Drone attacks are widely associated with the fight against al-Qaida and its allies in neighboring Pakistan, where the unmanned aircraft are used to go after militants in areas where U.S. troops are banned from entering. But a NATO spokesman said the aircraft are also regularly used in Afghanistan.
"The use of drones is routine and drone strikes are something that we're able to rely upon when we need them," Lt. Nico Melendez said, adding that their use has not increased or decreased in recent months.
Melendez said drones are used in Afghanistan for reconnaissance, aerial monitoring and for attacks.
In the south-central part of the country, a member of the Afghan National Police was killed and two others were wounded in a suicide attack Monday evening at a police station in Uruzgan province, police chief Juma Gul Hamit said. The suicide bomber detonated his cache of explosives near the gate of the police chief's office in Dihrawud district.
Hamit said the attacker tried to enter the office where a meeting was under way. Although wounded by police, the bomber detonated his explosive vest, killing the one policeman and injuring the two others who kept him from going inside.
In Paris, meanwhile, the French military said an army captain died Tuesday of wounds suffered a day before during an insurgent ambush in the Alasay valley east of Kabul. Another French soldier was killed instantly in the same ambush.
Both casualties were with a joint Afghan and French army patrol that was attacked by small arms fire in a village market place.
France has some 3,500 troops with NATO in Afghanistan. It has lost 38 men in Afghanistan since 2001.