Obama sent a letter of apology to Afghan President Hamid Karzai expressing his "deep regret."
The letter delivered today by the U.S. ambassador to Afghanistan also said those responsible for the error will be held accountable.
NATO has also apologized and called the burnings at Bagram Air Base a mistake. Materials, including Qurans, were removed from a detainee center and set on fire because of apparent extremist inscriptions.
Meanwhile, two U.S. soldiers were reportedly killed in Afghanistan in the latest violence over the Quran burning.
A statement from the U.S.-led International Security Assistance Force (ISAF) says the troops were targeted by an individual wearing an Afghan National Army uniform.
It is not clear if the troops were killed in revenge for the burning of Qurans, but the attack occurred at a base outside of which a demonstration was taking place, a local official said.
Just hours earlier, the Taliban called on Muslims to attack NATO bases and convoys and kill soldiers in retaliation for the burning of Qurans and other Islamic religious material.
There have been marches and violent protests across the country.
At least seven people have died over the past few days with many injured in clashes with police.
The commander of ISAF has issued a directive saying that all coalition forces in Afghanistan will be trained in the proper handling of religious materials in the next couple of weeks.
This isn't the first time that Americans' treatment of the Quran have stirred up trouble overseas.
Last year, when Florida pastor Terry Jones burned a copy of the holy book, outraged Afghans filled the streets in protest.
At least 24 people were killed in angry demonstrations before the controversy faded away.