In a statement, the Marine Corps said it has not verified the origin or authenticity of the YouTube video. It also said the actions portrayed are not consistent with Marine values.
If verified the video could create a strong backlash in the Muslim world and beyond for the disrespectful actions it portrays.
A defense official, speaking on condition of anonymity to discuss a sensitive aspect of the matter, said the case will be referred to the Naval Criminal Investigative Service, the Navy's worldwide law enforcement organization.
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.