KABUL, Afghanistan — On a day President Obama personally apologized for the burning of Qurans at a U.S-run military base, violence over the incident escalated ominously with the killing of two American troops by an Afghan army soldier during a demonstration in eastern Afghanistan.

At least 13 people have been reported killed in unrest that erupted after Afghan laborers at the Bagram Air Field discovered late Monday that discarded Qurans were being disposed of in the incinerator used to burn trash.

The fury appeared unabated despite the apology from Obama, reported Thursday by Afghan President Hamid Karzai's office. The presidential palace said a letter received from the U.S. president conveyed deep regret and offered assurances that "the error was inadvertent" and that those responsible would be held accountable.

Karzai met Thursday with parliamentarians, many of whom had been particularly vitriolic Wednesday in calling for Afghans to wage a holy war against international forces. He told the lawmakers they were right to raise their voices against the desecration of the Quran, but said a government investigation was the appropriate way to handle the case.

The statement said Karzai told the lawmakers that a U.S. officer responsible for the burning "didn't understand" what he was doing and that the United States had "accepted the mistake of its officer."

Anti-foreigner sentiment is never far below the surface in Afghanistan, and in the religiously conservative society, the episode triggered some of the most concerted expressions of outrage in years against the decadelong U.S. and Western presence. Foreign missions, including the U.S. Embassy, put sharp restrictions on the movement of personnel, and most international aid and development firms put their foreign staffs on lockdown.

The shooting deaths of the two U.S. troops took place at a base in the Khogyani district of Nangarhar province, said district governor, Mohammad Hassan. He said hundreds of protesters had gathered outside the base and were chanting anti-U.S. slogans when the attack took place. The assailant escaped into the crowd, he said.

Last April, two U.S. soldiers were shot and killed by a policeman in northern Afghanistan during a day marked by protests over an American pastor's intentional burning of the Quran. Days earlier, seven foreign U.N. workers were killed in the northern city of Mazar-i-Sharif in riots that resulted from the Florida evangelical church leader's action. At least nine Afghan civilians were also killed during protests in Kandahar, the spiritual home of the Taliban movement.

Previous Quran abuse incidents in the Guantánamo Bay, Cuba, prison and Iraq also led to wide-scale violence in Muslim nations. Then-President George W. Bush and senior military commanders apologized after a U.S. soldier in Iraq used a Quran for target practice in 2008.

NATO officials confirmed Thursday that a man in an Afghan army uniform had killed two of its service members in eastern Afghanistan but did not disclose their nationalities or provide details. Even before the current outbreak of unrest, turncoat shootings such as the one in Nangarhar province systematically eroded trust between Western and Afghan forces, with dozens of similar attacks taking place in the past two years.

The Taliban movement, which already had denounced the burning of Qurans as a "barbarous" act, issued new threats against Western troops. The group said members of the Afghan police and army should take advantage of their position to kill their ostensible allies whenever the opportunity arose.

Thursday marked the third straight day that Afghans took to the streets to express outrage over the burning of discarded copies of the Muslim holy book at the U.S.-run military installation north of Kabul. Afghan laborers on Monday found bags of Qurans among the trash bound for the giant incinerator and were able to prevent some copies from being burned, while displaying the remains of others.

A joint U.S.-Afghan investigation into the incident is under way and Western troops across Afghanistan are undergoing training on the proper handling of religious materials.

Material from The Associated Press is included.