In Jalalabad, the capital of Nangarhar province, hundreds gathered near the local airport. In Kabul, about 400 to 500 people rallied, including university students who marched toward the parliament building.
In Kandahar in the related demonstration, three people were killed in one demonstration, and nine in another when police and stone-throwing demonstrators clashed.
A U.S. warden message said more protests are possible in "coming days," adding that "past demonstrations in Afghanistan have rise into violent attacks on Western targets of opportunity."
The copies of the Quran were part of religious materials removed from the library of a detainee center at Bagram Airfield, a military official said.
Gen. John Allen, commander of NATO's International Security Assistance Force, said the materials were gathered for disposal and inadvertently given to troops for burning.
"This was not a decision that was made because they were religious materials," he said. "It was not a decision that was made with respect to the faith of Islam. It was a mistake. It was an error. The moment we found out about it, we immediately stopped and we intervened."
He offered his apologies and issued a directive that all coalition forces in Afghanistan will undergo training no later than March 3 so they can identify religious materials and handle them correctly.
"This is not who we are. These are very, very isolated incidents," Allen said.
But Allen's words were not enough to appease angry Afghans who massed outside the Bagram base Tuesday.
"It was intolerant and it was extremely disrespectful and again, we condemn it in the strongest manner possible," said Gen. David Petraeus, who headed the U.S.-led international forces in Afghanistan at the time.
Afghans regard the Quran as the absolute word of God. It is so highly revered that many Muslims will not pick up the holy Quran without ablution, a custom washing of the hands.
Prepared by Ahmadi