BAGRAM, Afghanistan — Word that NATO personnel had burned an undisclosed number of Korans and were preparing to dispose of many more by incineration set off an angry protest here on Tuesday. NATO officials rushed to apologize publicly and profusely, trying to head off what they feared could be a nationwide outburst of violence as news of the burning was gradually broadcast across the country.

About 2,000 Afghans descended on the largest American air base in their country in the bitter cold to protest what is generally regarded as one of the most offensive acts in the Muslim world.

“I offer my sincere apologies for any offense this may have caused, to the president of Afghanistan, the government of the Islamic Republic of Afghanistan and, most importantly, to the noble people of Afghanistan,” the NATO commanding general, John R. Allen, said in a statement that was recorded and sent to local television and radio networks here, explaining that the burnings had been unintentional.