* Taliban calls on Afghan troops to kill Westerners
* Violent protests erupt for third straight day
* Two American troops killed, NATO compounds attacked (Releads with Afghanistan demanding trial)
By Mirwais Harooni and Amie Ferris-Rotman
KABUL, Feb 23 (Reuters) - Afghanistan wants NATO to put on public trial those who burned copies of the Koran at a NATO base, President Hamid Karzai's office said on Thursday, after a third day of bloody protests over the incident.
It said NATO had agreed to a trial, but that could not be immediately confirmed.
Karzai had earlier accused a U.S. officer of "ignorantly" burning copies of the Koran, in an incident that has deepened anti-Western sentiment in a country NATO is trying to stabilise before foreign combat troops leave by the end of 2014.
Demonstrations have drawn thousands of angry Afghans to the streets, chanting "Death to America!" amid violence that has killed 11 people including two U.S. service personnel.
"NATO officials, in response to a request for the trial and punishment of the perpetrators ... promised this crime will brought to court as soon as possible," Karzai's office said in a statement.
President Barack Obama sent a letter to Karzai apologising for the burning of the Korans, after Afghan labourers found charred copies while collecting rubbish at the sprawling Bagram air base.
Obama told Karzai the incident 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 U.S. Ambassador Ryan Crocker.
Karzai's office said in a statement Obama had promised to investigate those involved in the incident.
Karzai said the American officer had acted "out of ignorance and with poor understanding" of the Koran's importance, a presidential statement said.
The Taliban urged Afghan security forces to "turn their guns on the foreign infidel invaders", it said on its site shahamat-english.com.
A U.S. official in Washington said two NATO soldiers killed by a man in Afghan army uniform were Americans.
NATO confirmed a man in Afghan army uniform had killed two of its troops in the east, but declined to say if the shooting was connected to the protests.
Muslims consider the Koran the literal word of God and treat each copy with deep reverence. Desecration is considered one of the worst forms of blasphemy.
A protest of around 500 people turned violent in the capital Kabul, with police and plain-clothes intelligence officers charging demonstrators wearing bandanas and hurling rocks and sticks, firing low above their heads and sending them fleeing.
A wounded youth lay on a road, blood pouring from his side. Crouched over and cradling him, a relative appealed to the Afghan government.
"Ministry of the Interior! Don't you see we are fighting NATO?" said the man.
Masked men sped by on a motorcycle blasting a battle song played by the Taliban insurgency, while police in machinegun-mounted pick-up trucks picked up the wounded.
"Our brave people must target the military bases of the invaders, their military convoys and their invader forces," read an e-mailed Taliban statement released by the insurgency's spokesman Zabihullah Mujahid.
"They have to kill them (Westerners), beat them and capture them to give them a lesson to never dare desecrate the holy Koran again."
Most Westerners were confined to their heavily fortified compounds, including the sprawling U.S. embassy complex and other embassies in central Kabul.
Around 400 protesters hurled rocks and set fire to cars at a Norwegian-led military base in Faryab province on the Turkmen border, which is centre for around 500 soldiers and civilians from Norway, Latvia, Macedonia, Iceland and the United States.
Twelve protesters were wounded in the attack, the head of the regional hospital Abdul Alim said , but Norway's ambassador to Kabul, Tore Hattrem, told Reuters no one was hurt and there was minimal damage.
A small number protested at a French military base in the eastern Kapisa province but police deterred them successfully, its police chief Abdul Hamid said.
The uproar could complicate efforts by U.S. and NATO forces to reach agreement with the Afghan government on a strategic pact that would allow a sharply reduced number of Western troops to stay in the country, well beyond their combat exit deadline, to oversee Afghan forces.
Hundreds of protesting students in Jalalabad rejected any strategic pact with the United States, saying they would "take up jihad" if one were sealed. (Additional reporting by Mohammad Hamid in Kunduz, Rafiq Shirzad in Jalalabad, Akram Walizada and Omar Sobhani in Kabul and Elyas Wahdat and Obaidullah in Logar; Writing by Amie Ferris-Rotman and Rob Taylor; Editing by Michael Georgy, Ed Lane and Andrew Roche)