The move by U.S. Army Lt. Gen. Curtis M. Scaparrotti came in response to a YouTube video posted this week showing four U.S. Marines urinating on bodies of suspected Taliban fighters.
In a letter to NATO's Kabul-based International Security Assistance Force Joint Command, Scaparrotti wrote: "Defiling, desecrating, mocking, photographing or filming for personal use insurgent dead constitutes a grave breach" of the laws of armed conflict. "We must treat the living and dead with dignity and respect."
Investigators have identified the four Marines who appear in the video but their names haven't been released, Maryann Cummings, a spokeswoman for the Naval Criminal Investigative Service, told CNN.
NCIS agents have interviewed the Marines, who have been released to the agents' command, the Marine Corps Times said.
No criminal charges have been filed so far.
Lt. Gen. Thomas D. Waldhauser, commander of the Marine Corps' Central Command, which oversees all Marine operations in Iraq and Afghanistan, will serve as lead investigator, The New York Times reported. He will conduct a criminal investigation into actions of the four Marines and possibly others, and an inquiry into leadership issues and factors leading to the incident.
In a statement, the Marines said "an expeditious, full and fair investigation will be conducted, and appropriate action will be taken in response to this incident."
The four Marines, all now in the United States, are with the 3rd Battalion, 2nd Marines, out of Camp Lejeune, N.C.
The video is believed to have been taken in 2010 in Helmand province, where the battalion had operated during its deployment, the Times said.