All four US Marines seen in a video apparently urinating on dead Afghans have been identified by American military investigators, US media say.
Two of the men have already been interviewed by the US Navy's criminal investigation branch.
The Marine Corps has also appointed Lt Gen Thomas Waldhauser, a three-star general, to decide what, if any, disciplinary action is to be taken.
It is understood the troops served in Helmand province, Afghanistan.
US media reported that the unit belonged to the 3rd Battalion, 2nd Marine Regiment, but that two of the men and the battalion's commander had moved on to other assignments before the video became public.
The names of the men, who are thought to be Marine snipers, have not been released.
The battalion has had a range of deployments, including Iraq, Afghanistan, Guantanamo Bay and fighting wildfires in the US state of Idaho.
Marine General John Allen, the top US and Nato commander in Afghanistan, called for the facts of the case to be established quickly.
He said: "These actions are in direct opposition to everything the military stands for. Such acts in no way reflect the high moral standards and values we expect of our armed forces on a daily basis."
Lt Gen Waldhauser will appoint another officer to lead the Marine Corps' internal investigation into the incident.
In addition, the Naval Criminal Investigative Service is undertaking its own probe of the matter.
Lt Gen Waldhauser is responsible for deciding on the course of action after both investigations have been completed.
Correspondents say that, if authentic, the actions in the video could amount to a violation of the First Geneva Convention, which calls for the dead to be treated with dignity.
It could also constitute a breach of the US Uniform Code of Military Justice, for discrediting the armed forces.
The video, which was posted online, appears to show the troops standing over the bodies of several Afghans, at least one of whom is covered in blood.
A man's voice is heard saying: "Have a great day, buddy."
The clip has been called "disgusting" and "inhuman" by both US and Afghan officials.
US Secretary of State Hillary Clinton expressed her "dismay" at the images, while Afghan President Hamid Karzai requested the "most severe punishment" for those responsible.
In an address to military personnel at Fort Bliss, Texas, on Thursday, US Defence Secretary Leon Panetta said the video could even jeopardise the prospects for US-Afghan peace talks.
The Taliban have indicated that while they condemn the video, its release would not affect the political process.
Fears that widespread outrage in Afghanistan would boil over into protests immediately after Friday prayers proved unfounded.
But one Kabul resident, 20-year-old construction worker Waheedullah, who like many Afghans uses only one name, told AFP news agency: "This is an absolutely savage act and condemnable in any religion."
It is not clear who released the footage, which first appeared on YouTube and has not been verified.
The US has about 20,000 Marines in Afghanistan, based mostly in the provinces of Kandahar and Helmand. In total, about 90,000 US troops are on the ground in Afghanistan.