"This disrespectful act is inexplicable and not in keeping with the high moral standards we expect of coalition forces," the International Security Assistance Force said a statement.
The ISAF said the actions "appear to have been conducted by a small group of U.S. individuals, who apparently are no longer serving in Afghanistan." The statement did not identify the personnel or explain why the ISAF thought they had left the country.
The Marine Corps said Wednesday it is investigating the YouTube video but has not yet verified its origin or authenticity. The case has being referred to the Naval Criminal Investigative Service, the Navy's worldwide law enforcement organization, said NCIS spokesman Ed Buice.
The Council on Islamic-American Relations, a prominent Muslim civil rights and advocacy group based in Washington, quickly condemned the video.
"We condemn this apparent desecration of the dead as a violation of our nation's military regulations and of international laws of war prohibiting such disgusting and immoral actions," the group wrote in a letter faxed to Defense Secretary Leon Panetta.
"If verified as authentic, the video shows behavior that is totally unbecoming of American military personnel and that could ultimately endanger other soldiers and civilians," the letter said.
Marine Corps headquarters at the Pentagon said, "The actions portrayed are not consistent with our core values and are not indicative of the character of the Marines in our Corps. This matter will be fully investigated."
A Marine Corps spokesman, Lt. Col. Stewart Upton, added, "Allegations of Marines not doing the right thing in regard to dead Taliban insurgents are very serious and, if proven, represent a failure to adhere to the high standards expected of American military personnel."
A Pentagon spokesman, Navy Capt. John Kirby, said the video is deeply troubling.
"Whoever it is, and whatever the circumstances -- which we know is under investigation -- it is egregious behavior," Kirby said.
It is unclear who shot the video and who posted it online.