The alleged incident was apparently filmed by a freelance photojournalist embedded with a US Army unit in the hills near the southern city of Kandahar this month. Its authenticity does not appear to be in serious question.
US military commanders in Afghanistan called the episode "repugnant". They said the Army's criminal investigation division was considering charges that included "burning of dead enemy combatant bodies under inappropriate circumstances". In Kabul, the Afghan government of Hamid Karzai insisted that those responsible must be punished. "We strongly condemn any disrespect to human bodies, regardless of whether they are those of enemies or friends," a spokesman said.
The footage, aired by the Australian SBS network, was taken by Stephen Dupont, an Australian journalist with the 173rd Airborne Brigade. It shows a group of soldiers watching as two corpses a few yards away are consumed in flames.
Two soldiers with American accents then reportedly sent taunting messages apparently directed at a nearby village the soldiers seemed to believe had been sheltering the insurgents.
"You allowed your fighters to be laid down facing west and burnt," one message allegedly ran. "You are too scared to come down and retrieve their bodies." The broadcast, organised by the Army's psychological operations unit, refers to the Taliban as "cowardly dogs".
Mr Dupont said the messages were broadcast in the local language, and translated into English for him by psy-ops troops. The video showed military vehicles fitted with speakers and playing loud music.
The circumstances are a direct violation of Islamic tradition in Afghanistan, where the dead are buried with their heads pointing north, their feet south, and only their faces turned to Mecca in the west. Nor is cremation a Muslim custom; bodies are normally washed, wrapped in white cloth and buried within 24 hours of death.
The Geneva Conventions stipulate that enemy dead should be honourably interred.
Ahmad Fahim Hakim, deputy head of Afghanistan's Independent Human Rights Commission, said body-burning was "outrageous", and the US was "ignoring the basic principles of international humanitarian law".
Faiz Mohammed, one local figure, warned: "This is against Islam. Afghans will be shocked by this news. It is so humiliating, and there will be very dangerous consequences from it."
Muslims have been angered by a litany of controversies, ranging from reports of brutal treatment of prisoners by the military, the alleged desecration of the Koran at the Guantanamo Bay prison in Cuba and the shocking abuse at Abu Ghraib jail in Iraq. All have been interpreted across the Muslim world as proof that the US holds Islam in contempt.
Not only has damage to America's image been immense; five months ago, the Koran claims provoked anti-US riots in Afghanistan, in which 15 people died.
Mr Dupont said the soldiers told him they were burning the bodies "for hygienic reasons". But, in an interview with the Australian network, he said broadcasts later by the psychological unit showed it was aware the cremation was a desecration.
"They used that as psychological warfare, I guess you'd call it," Mr Dupont said. "They deliberately wanted to incite that much anger from the Taliban so the Taliban would attack them. That's the only way they can find them."
Local police say Taliban fighters are hiding in their hundreds in camps in the region where the two bodies were burnt. "We go there only with American troops," Abaidullah Khan, the district police chief, said. "It's not safe otherwise."
A State Department spokesman said: "These are very serious allegations. If there is wrongdoing, those responsible will be held to account."Reuse content