President Barack Obama has apologised over the burning of Qurans by Nato troops at a US base in Afghanistan, calling it an inadvertent error, the Karzai's office said on Thursday.
"We will take the appropriate steps to avoid any recurrence, including holding accountable those responsible," the CNN quoted Obama as saying.
The apology came as the Taliban called on Muslims to attack Nato military bases and convoys and kill its soldiers following the admission that Nato troops had incinerated Islamic religious material at Bagram Airfield.
According to the BBC, Obama's letter assured the Afghan president that US authorities would question all those responsible.
"I convey my deep sympathies and ask you and the people to accept my deep apologies," the letter said.
President Karzai told members of the Afghan parliament that a US officer was responsible for the burning.
But Karzai said it was done out of "ignorance".
Meanwhile, demonstrations against the desecration continued for a third day across northern and eastern Afghanistan.
Two foreign soldiers, believed to be Americans, have been killed, along with at least six Afghan people.
On Wednesday, another seven people were killed and dozens injured in protests.