Mohammad Rahim Amin, chief of the Baraki Barak district in eastern Logar province, said the deaths and injuries occurred when Afghan soldiers opened fire on hundreds of protesters who were trying to storm the local government headquarters.
During recent protests against the Quran burning, Afghans have regularly targeted the pro-Western government.
Terry Jones, pastor of a small Florida church, said Saturday that "we feel that God is telling us to stop" the Quran burning, which was to coincide with the ninth anniversary of the Sept. 11, 2001, attacks in the United States.
The plan to burn the Quran stirred outrage among millions of Muslims and others worldwide.
The protesters in Logar chanted "Death to America" and burned tires, attacked several shops and set election campaign posters on fire, Amin said.
"I can say for sure that this was the work of the enemies of peace and stability in Afghanistan who are trying to use any opportunity to disrupt the security situation" in the country, Amin said.
In a country where most people have limited access to newspapers, television and the Internet, many Afghans seemed unaware of Jones' decision to call off the Quran burning.
Meanwhile, a Taliban commander who planned rocket attacks on polling stations during elections next week and four other insurgents were killed in eastern Afghanistan, NATO said Sunday.
The military alliance said NATO and Afghan forces killed the five insurgents Saturday night in a village compound in the eastern Nangarhar province. The insurgents were killed after they "displayed hostile intent" as the forces moved in on the compound, it said in a statement.
It said intelligence reports indicated the Taliban commander was planning to conduct rocket attacks on voting centers during the Sept. 18 parliamentary elections. The Taliban has vowed to target polling stations and warned Afghans not to participate in what it called a sham vote.
The government and its Western allies hope the elections for the lower house of parliament will help consolidate the country's fragile democracy, leading to the withdrawal of the roughly 140,000 NATO-led foreign troops in the country. But many Afghans and foreign observers fear the vote could turn bloody if the Taliban carries out its threats.
"The Afghan people deserve to cast their votes without fear of attacks from the insurgent groups," U.S. Army Col. Rafael Torres said in the NATO statement. "We are tracking them and taking action before they're able to carry out their plans."
NATO said the killed Taliban commander had participated in "intimidation campaigns and assassinations" and was directly linked to a February suicide bomb attack that killed Haji Zaman, a well-known tribal elder and warlord in eastern Afghanistan.
More Coverage Marking the 9th Anniversary of 9/11:
Obama: 9/11 Victims Endure in Our Nation's Heart
President Obama Speaks at Pentagon Memorial
Biden Speaks on 9/11 at Ground Zero
Michelle Obama Remembers Flight 93
Laura Bush Speaks at Flight 93 Memorial
Islam Controversies Cast Shadow Over 9/11 Events
Proposed Islamic Center Divides 9/11 Families
NYC More Ready for Huge Disaster Than on 9/11?
Muslim Scholar: Don't Build Islamic Center
Pastor on Quran Burning: "Not Today, Not Ever"
Obama Remembers Sept. 11, Calls for Unity
Rebuilding Ground Zero
By Associated Press Writer Dusan Stojanovic. Rahim Faiez contributed to this report