President Barack Obama sent a letter to Afghan President Hamid Karzai on Thursday apologising for the burning of copies of the Quran at a US military base in Afghanistan, the White House said.

Obama told Karzai the incident, which has sparked angry protests against US and NATO forces in Afghanistan, was not intentional.

The letter, which the White House said was a follow-up to a phone call earlier this week between the two leaders to discuss a "long-term partnership" between Washington and Kabul, was delivered to Karzai by US Ambassador Ryan Crocker.

"In the letter ... the president also expressed our regret and apologies over the incident in which religious materials were unintentionally mishandled at Bagram Airbase ," White House spokesman Tommy Vietor said.

The Taliban urged Afghans to target foreign military bases and kill Westerners in retaliation for the Quran burning at Bagram airfield near Kabul on Tuesday.

NATO confirmed a man in Afghan army uniform killed two of its troops in the east on Thursday, but declined to say if the shooting was connected to the protests.

The Quran burnings could make it even more difficult for US-led NATO forces to win the hearts and minds of Afghans and bring the Taliban to the negotiating table ahead of the withdrawal of foreign combat troops by the end of 2014.

The US government and the American commander of NATO-led forces in Afghanistan had already apologised for the burnings after Afghan labourers found charred copies of the Koran while collecting rubbish at Bagram.