The video, which was posted online, purports to show four US Marines standing over the bodies of several Taliban fighters, at least one of whom is covered in blood.
The Marines have begun a criminal investigation and an internal inquiry.
US officials and Afghan officials have condemned the video as “deplorable”.
The origin of the video is not known, but it was originally posted to YouTube.
US media reported that the unit belonged to the 3rd Battalion, 2nd Marine Regiment.
That battalion has been deployed to a wide range of combat a peacekeeping situations, from Iraq, Afghanistan and Guantanamo Bay to fighting wildfires in Idaho.
The unit deployed to Afghanistan in early 2011 and returned in September or October, CNN reported.
A US Marines spokesman, Lt. Col. Joseph Plenzler, told the AFP news agency that “we cannot release the name of the unit at this time since the incident is being investigated.”
Earlier, US Defence Secretary Leon Panetta condemned the acts shown in the video and vowed that a full investigation would be carried out by the Marines and the Kabul-based International Security Assistance Force (Isaf).
“This conduct is entirely inappropriate for members of the United States military,” Leon Panetta said in a statement.
Hamid Karzai condemned the attacks in strong terms.
“I find the behaviour depicted in it utterly deplorable. This conduct is entirely inappropriate for members of the United States military,” Hamid Karzai said.
In a separate news conference, Secretary of State Hillary Clinton expressed her “total dismay” at the video.
Hillary Clinton said she shared Leon Panetta’s view that such behaviour was inconsistent with the standards “that [the] vast, vast majority of our personnel – particularly our marines – hold themselves to”.
“The video did not change the nature of US efforts to secure Afghanistan,” Hillary Clinton said. She also said the US continued to support security and reconciliation efforts that were “Afghan-led and Afghan-owned”.
The Taliban are known for applying a ruthless brand of Islamic Sharia law in areas they control and have carried out many suicide bombings and attacks which have killed civilians.
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