The U.S. Marines Corps has identified all four of the men seen urinating on the corpses of insurgent fighters in a viral video that emerged this week ... and they are all part of a sniper team based in North Carolina.

According to reports, all four members belong to the 3rd Battalion, 2nd Marines, which returned to the U.S. last fall after a tour in Afghanistan ... after 7 members of the 1,000-person battalion were killed in action.

So far, the names of the men have not been released.

CBSNews.com reports the men had been showing off the video as a "war trophy" at their home base in Camp Lejeune in NC.

At least two of the Marines have been interviewed by USMC officials -- but are not being detained.

A rep for the White House says President Barack Obama is aware of the video -- but would not say if he has actually seen it yet.

Hillary Clinton has condemned the video -- calling the action "deplorable behavior."

Muslim organizations across the United States tell TMZ they are outraged by the disturbing footage which appears to show Marines urinating on the bodies of dead Taliban fighters.

"We are appalled by the video" ... a rep for the Muslim Public Affair Council tells us ... adding, "We ask Secretary of Defense Leon Penetta to reprimand these soldiers. These soldiers don’t stand for what our nation and our army and armed forces fight for on a daily basis."

The Washington-based Council on American-Islamic Relations (CAIR) had a similar opinion -- saying, "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."

CAIR adds, "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."

TMZ broke the story ... the U.S. Marine Corps is conducting an investigation into the footage to find out when the video was shot, where it was shot and if the men are indeed U.S. Marines.

The United States Marine Corps is launching an investigation into a video which appears to show Marines in full combat gear urinating on several dead bodies ... TMZ has learned.

In the extremely graphic video, which appeared on various websites this morning, at least 4 male Marines expose their genitals and urinate on the bodies.

The mystery person who posted the video included a caption that reads, "scout sniper team 4 with 3rd battalion 2nd marines out of camp lejeune peeing on dead talibans."

Now, Captain Kendra N. Hardesty -- a Media Officer for the USMC -- tells us, "While we have not yet verified the origin or authenticity of this video, the actions portrayed are not consistent with our core values and are not indicative of the character of the Marines in our Corps."

She adds, "This matter will be fully investigated and those responsible will be held accountable for their actions."

In the video, one of the urinating men can be heard saying, "Have a great day, buddy."

Another guy jokes about the situation ... saying, "Golden like a shower."