A presidential statement described the act as "completely inhumane" and called on the U.S. military to punish the Marines.

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.

The Afghan Ministry of Defense also condemned the actions in the video, which it described as "shocking."

The NATO-led security force in Afghanistan released a statement Thursday saying, "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 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.

Sen. John McCain, a Navy veteran who fought in the Vietnam war, said the incident "makes me so sad."

McCain, the top Republican on the Senate Armed Services Committee, called the Marine Corps one of America's strongest institutions and said its image has apparently been tarnished by "a handful of obviously undisciplined people."

Appearing Thursday on "CBS This Morning," the Arizona Republican said, "There should be an investigation and these young people should be punished."

On Wednesday, the Council on Islamic-American Relations, a prominent Muslim civil rights and advocacy group based in Washington, protested the video in a letter faxed to Defense Secretary Leon Panetta.

"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.

"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.