"Two of the culprits and their unit involved in the shameful act have been identified," CNN reported quoting a Pentagon spokesman.
"We cannot release the names of the unit as well as the culprits at this time as the matter is being investigated," a Marine spokesman told CNN referring to the video which has gone viral sparking outrage and unrest in Afghanistan and the wider Muslim world.
The unit was deployed to Afghanistan mainly in Helmand province in early 2011 and had returned home in September or October, the TV channel said.
The US cable network quoted a Marine officer saying that the military was "confident that troops involved in the inflammatory video were from the third Battalion of the second Marine regiment based at Camp Leteune, North Carolina."
The video appeared to show four servicemen urinating on three bloodied corpses and one of them apparently aware that they were being filmed saying "Have a great day buddy", referring to one of the dead.
Defence Secretary Leon Panetta has said those found engaged in such conduct will be held accountable to the fullest extent.
"This conduct is entirely inappropriate for the US military and does not reflect the standards of values our armed forces are sworn to uphold," he said in a statement.
Earlier, the White House deplored the video.
"We find this - we've seen the video, and what it depicts is - or what it apparently depicts is deplorable, reprehensible and unacceptable," White House Press Secretary Jay Carney said.
The video, posted on YouTube and other websites, is a big embarrassment for the Obama Administration, especially at a critical time of holding peace talks with the Taliban.
The Department of Defence has ordered a probe into the authenticity of the video as well as those who were responsible for this.
"The alleged action is obviously under investigation," Carney said in response to a question.
He referred to the telephone call made by Defence Secretary Panetta to Afghan President Hamid Karzai, in this regard, in which he vowed to hold accountable to all those responsible for this, if the video is found to be authentic.
"I don't know whether or not the President has actually seen the video. He is certainly aware of it and shares the sentiment expressed by Secretary Panetta," Carney said.
"Certainly what is apparently occurring in that video is deplorable and does not live up to the very high standards set for the US Marines or, broadly, the US military," he said.
Secretary of State Hillary Clinton joined Panetta in deploring the video, saying "it is absolutely inconsistent with American values, with the standards of behaviour that we expect from our military personnel."
In a statement Gen Martin Dempsey, Chairman of the Joint Chiefs of Staff, said he is deeply disturbed by the actions in this video.
"Actions like those are not only illegal but are contrary to the values of a professional military and serve to erode the reputation of our joint force. The Marine Corps has asked NCIS for a thorough investigation and I am confident that there will be accountability, as appropriate," Dempsey said.