Obama`s letter to Karzai in this regard was delivered by US Ambassador to Afghanistan, Ryan Croker, this afternoon, National Security Council spokesman, Tommey Vietor, said.
"Following up on their February 20 phone call, the President sent a letter to President Karzai to continue their discussion on a range of issues related to our long-term partnership," Vietor said.
"In the letter, delivered by Ambassador Crocker this afternoon in Kabul, the President also expressed our regret and apologies over the incident in which religious materials were unintentionally mishandled at Bagram Airbase," Vietor said.
The burning of copies of the Quran at the Bagram base north of Kabul has sparked three days of fierce anti-US protests in Afghanistan in which at least 12 protesters have been killed.
Later in a gaggle, the White House Press Secretary, Jay Carney, said Obama following up on a telephone conversation wrote a long letter on a variety of issues related to its bilateral engagement, including reconciliation, including the trilateral talks that they had with Pakistan last week in Islamabad.
"He also expressed his apology for the inadvertent burning of religious materials by American personnel in Afghanistan. It is wholly appropriate given the understandable sensitivities to this issue," Carney said.
"His primary concern as commander in chief is the safety of American men and women in Afghanistan, of our military and civilian personnel there. It`s absolutely the right thing to do," he said.
Carney said Karzai did not ask for the letter, which "is not appropriate to show" to reporters.