Announcing an inquiry, US Gen John R Allen said any "improper disposal" of religious materials was inadvertent.
Reports suggest the books were taken from prisoners after the US uncovered a secret Taliban message system.
Rumours that a Koran had been burnt led to protests outside the US base at Bagram north of Kabul. One man was hurt when Nato troops fired rubber bullets.
President Hamid Karzai condemned the reports that the Koran had been burnt, as did the Taliban who said the incident would hurt the feelings "of one billion Muslims around the world".
US Defence Secretary Leon Panetta called the incident "inappropriate and deeply unfortunate".