Afghanistan's government has demanded that those responsible be punished and top Muslim clerics have warned that anti-American demonstrations may break out.
Australia's SBS television network broadcast video footage that purportedly showed US soldiers burning the bodies of the suspected Taliban fighters in the hills outside the southern village of Gonbaz, near the former Taliban stronghold of Kandahar.
The network said the footage was taken by a freelance journalist, Stephen Dupont, who told The Associated Press he was embedded with the 173rd Airborne Brigade of the US army earlier this month.
Dupont said the burnings happened on 1 October.
In the footage, which was seen by the AP, two soldiers who spoke with American accents later read taunting messages that the SBS said were broadcast to the village, which was believed to be harbouring Taliban soldiers.
Dupont said the soldiers responsible for the taunting messages were part of a US army psychological operations unit.
"They used that as a psychological warfare, I guess you'd call it. They used the fact that the Taliban were burned facing west. They deliberately wanted to incite that much anger from the Taliban..."
The US military said on Thursday the Army Criminal Investigation Division had opened an investigation into alleged misconduct that included "the burning of dead enemy combatant bodies under inappropriate circumstances".
"This alleged action is repugnant to our common values," Major General Jason Kamiya said in a statement from the US base in Bagram, Afghanistan.
"This command takes all allegations of misconduct or inappropriate behaviour seriously and has directed an investigation into circumstances surrounding this allegation."
Muslim clerics warned protests might break out like the violent anti-American riots in May that killed 15 people. "This is against Islam. Afghans will be shocked by this news. It is so humiliating," said Faiz Mohammed, a Muslim leader. "There are very, very dangerous consequences from this. People will be very angry."
General Mohammed Zahir Azimi, spokesman for the Afghan Defence Ministry, said those responsible must be punished.
Muslim clerics warn the incident
may incite anti-US protests
Shortly after the bodies were burned, the soldiers from the psychological operations unit allegedly read out taunting messages about the act over a loudspeaker to the nearby village, according to a transcript of the programme.
"Taliban, you are all cowardly dogs. You allowed your fighters to be laid down facing west and burned. You are too scared to come down and retrieve their bodies," said one message read by a soldier, according to the transcript.
Against Islamic tradition
The footage did not show the messages being broadcast, though it did show some military vehicles were fitted with speakers and playing loud music.
Dupont told the AP the messages had been broadcast in the local dialect but were translated into English for him by members of the army psychological operations unit.
He declined to provide further information, however, saying his agent was now handling all queries about the footage.
Cremation of bodies is not part of Muslim tradition, which calls for remains to be washed, prayed over, wrapped in white cloth and buried within 24 hours.
Dupont said the soldiers who burned the bodies said they did so for hygiene reasons.
However, Dupont said the incendiary messages later broadcast by the US army psychological operations unit indicated they were aware that the cremation would be perceived as a desecration.
"They used that as a psychological warfare, I guess you'd call it. They used the fact that the Taliban were burned facing west (towards Makka)," Dupont told SBS.
"They deliberately wanted to incite that much anger from the Taliban so the Taliban could attack them. That's the only way they can find them."
The SBS report suggested the deliberate burning of bodies could violate the Geneva Conventions governing the treatment of enemy remains in wartime.
Under the Geneva Conventions, soldiers must ensure that the "dead are honourably interred, if possible according to the rites of the religion to which they belonged".
Furthermore, the rules state that bodies should not be cremated, "except for imperative reasons of hygiene or for motives based on the religion of the deceased".