The protests spread from Kabul to eastern Afghanistan as angry Afghans reacted to news of the burning of the Muslim sacred text at Bagram Air Base.
Wednesday's demonstration came on the heels of protests Tuesday and rumors NATO personnel were preparing to dispose of more Korans.
CNN reported at least five people died and others were injured in Wednesday's violence. Of those, one died in Kabul, the U.S. news network said. The other four died in Parwan province in police firing, CNN reported, quoting a provincial official.
The report said at least 11 protesters were injured in Kabul and 10 more in eastern Nangarhar province.
CNN said about 400 to 500 protesters burned tires and threw rocks outside Camp Phoenix near the Kabul International Airport.
The U.S. Embassy in Kabul went into lockdown and all travel by staff was suspended, The New York Times reported.
"The embassy is on lockdown; all travel suspended. Please, everyone, be safe out there," an embassy Twitter post said.
The report said NATO soldiers were keeping military vehicles off the streets in Kabul.
In Jalalabad in eastern Afghanistan, protesters tried to break into the NATO base and later set fire to six fuel tankers in a nearby parking lot, the Times said.
The protest in Kabul saw people shouting anti-American slogans and throwing stones at Afghan army vehicles.
NATO Commander Gen. John Allen, in a recorded statement Tuesday, said the Koran burning was not intentional.
Also on Tuesday, U.S. Defense Secretary Leon Panetta joined General Allen in apologizing for the improper and inadvertent disposal of the religious items. White House spokesman Jay Carney called it a "deeply unfortunate incident," and "we apologize to the Afghan people and disapprove of such conduct in the strongest possible terms."
The Times said Afghan President Hamid Karzai Wednesday condemned the Koran burning and announced an investigation.
The Times said reports by witnesses at the burning and religious leaders who met with NATO officials at Bagram indicated some copies had been pulled from the flames before they were badly damaged.
CNN, quoting a military official, said copies of the Koran and other religious materials apparently were removed from the library of a detainee center at Bagram on concerns inscriptions on them might be used for communication by extremists.
The apologies came amid concern among NATO officials the protest could spread across the country, triggering violence.
Allen's "sincere apologies" were conveyed to the Afghan government, its president and "most importantly, to the noble people of Afghanistan."
Allen also ordered an investigation and asked every coalition soldier to complete a 10-day training course on "the proper handling of religious materials," the Times reported.