Habibullah Jan, another protester said: "We have proof that they destroyed our holy Quran. We can show them to [President Hamid] Karzai's government or the foreign forces."
A security official in the province said six people were killed in the shooting, but said they were investigating to find out whether they were civilians or Taliban-linked fighters.
The Nato-led International Security Assistance Force (Isaf), however, has rejected the allegations, saying Afghan forces backed by coalition troops had conducted an operation in the area on Sunday, but not a shot was fired and no one was detained.
"The joint force protected the dignity of all innocent civilians during the operation," the Isaf statement said.
The statement said an Afghan official was shot during Tuesday's protest, adding that "Isaf service members identified the insurgent sniper, shot and killed him. There were no other injuries or shots fired," it said.
Major General Michael Regner, an Isaf spokesman, said: "As partners with the Afghan people, we will thoroughly investigate allegations to determine the facts."
Hundreds of people protested against US forces last year after claims that troops desecrated the Quran in the central province of Wardak in October.
Both the Afghan and US officials rejected the allegations and said it was part of Taliban propaganda to provoke public anger against the international forces in the country.
There are more than 110,000 international troops currently in the country including around 68,000 US troops.
As part of a military escalation to turn the tide against the Taliban fighters, the US government has planned to send 30,000 additional soldiers by summer.