In a statement, Gen John R Allen ordered a full investigation.
"When we learned of these actions, we immediately intervened and stopped them," he said.
Rumours that a Koran had been burnt led to a large protest outside the US air base at Bagram about 60km (40 miles) north of Kabul.
Police told the BBC that at least 1,000 people took part in the demonstration, which has now ended, and that some elders went into the base to talk to Nato officials.
Afghan officials told the AP news agency that the Korans were in rubbish that two soldiers with the US-led coalition transported in a lorry late on Monday night to a pit on the base where waste is burned.
When five Afghans working at the pit noticed the religious books in the rubbish, they stopped the disposal process.
"Foreign troops tried to burn a container of holy Koran books at three o'clock in the morning, but the Afghan mujahideen employees working at the base did not allow them," protester Mohammad Zahir told the BBC.
A BBC reporter at the protests said he saw people crying over claims that foreign troops had set fire to the Koran, while others threw stones and fire bombs at the security forces.
A photographer for the AFP news agency said that guards at the base fired rubber bullets from a watchtower as the crowd shouted "Allahu akbar, Allahu akbar" (God is great).
'Sincere apologies'
In his statement, Gen Allen said that the investigation would examine whether troops at Bagram air base "improperly disposed of a large number of Islamic religious materials which included Korans".
"The materials recovered will be properly handled by appropriate religious authorities," the statement said.
"We are thoroughly investigating the incident and we are taking steps to ensure this does not ever happen again. I assure you… I promise you… this was not intentional in any way."
Gen Allen went on to offer his "sincere apologies for any offence this may have caused", to the president of Afghanistan, the Afghan government and "the noble people of Afghanistan".
Later, the Nato-led International Security Assistance Force (Isaf) force said it intended to invite Afghans to join the investigation "so we are transparent with this issue".
"These were religious materials that were gathered up at the detention facility in Parwan [province, where Bagram is located] and inadvertently given to troops for burning," the Isaf statement said.
"We are still trying to determine if and/or how much got burned before the mistake was discovered.
"If a Koran was damaged, we will find out how it happened and make certain that this does not happen again."
Correspondents say that it was a remarkably candid statement by Gen Allen - played repeatedly on Afghan television - apparently aimed at damage limitation after similar incidents led to violence and attacks on foreigners.
Kandahar Governor Tooryalai Wesa strongly condemned the alleged Koran destruction, which he described as a "shameful move by some stupid individuals".
The BBC's Andrew North, in Kabul, says that reports of the Islamic holy book being mistreated, whether substantiated or not, have proved incendiary in Afghanistan in the past.
The Taliban and other groups have sometimes been accused of spreading such reports to spark violence, but last year at least 10 UN workers were killed and dozens of other people injured in protests triggered by news of an American preacher setting the Koran on fire in Florida.