Washington (CNN) -- Two of the four Marines shown in a video urinating on dead bodies sprawled out on the ground have been identified by the Marine Corps, a Marine Corps official told CNN Thursday.
The names are not being made public, said the official, who did not want to be identified because the investigation is ongoing.
The identities were determined as officials in the United States and Afghanistan expressed shock and outrage regarding the video, which was posted Wednesday to a number of websites.
"I have seen the footage, and I find the behavior depicted in it utterly deplorable," U.S. Defense Secretary Leon Panetta said in a statement. "I condemn it in the strongest possible terms."
Panetta said he has ordered the Marine Corps and International Security Assistance Force Commander Gen. John Allen "to immediately and fully investigate the incident."
"This conduct is entirely inappropriate for members of the United States military and does not reflect the standards of values our armed forces are sworn to uphold," Panetta's statement said. "Those found to have engaged in such conduct will be held accountable to the fullest extent."
A senior Pentagon official said Panetta was "deeply troubled" after viewing the video.
Marine Corps Commandant Gen. James Amos said in a statement the behavior is "wholly inconsistent with the high standards of conduct and warrior ethos that we have demonstrated throughout our history."
Lt. Gen. Adrian Bradshaw, deputy commander of ISAF, called the actions on the video "disgusting."
"Any acts which treat the dead, enemy or friendly, with disrespect are utterly unacceptable and do not represent the standards we expect of coalition forces," Bradshaw said in a video statement. He said he was speaking on behalf of Allen, who is out of the country.
"It is difficult to say what long-term impacts this might have, and I would hesitate to get into speculation, but obviously any sort of footage, any sort of activity of this kind that is grossly against all the moral values that the coalition forces are standing for are very much working against our cause and against everything that we are standing for and that we are here for," said Brig. Gen. Carsten Jacobson, a NATO ISAF spokesman. "We will find the ones who are responsible and hold them accountable."
An earlier statement from NATO-led forces in Afghanistan said, "ISAF strongly condemns the actions depicted in the video, which appear to have been conducted by a small group of U.S. individuals, who apparently are no longer serving in Afghanistan."
A senior U.S. military official said the Naval Criminal Investigative Service is the lead investigative agency on the incident. A Marine Corps investigation was announced Wednesday.
While the identities of the people on the video haven't been released, the leadership of the 3rd Battalion 2nd Marine Regiment "is confident those are their Marines" on the video, according to a U.S. Marine official with direct knowledge of the initial investigation. Commanders are "not able to put names to Marines yet, but confident they fall under the 3/2," the official said.
The unit, which is based at Camp Lejeune, North Carolina, deployed last February or March and returned in September or October. While in Afghanistan, the unit was based primarily in Helmand province.
The video shows four men dressed in Marine combat gear urinating on what appeared to be the dead bodies of three men on the ground in front of them.
One of the men says, "Have a great day, buddy." A voice asks, "You got it on the video?" to which another voice responds, "Yeah." Another jokes, "Golden, like a shower."
It was not clear who shot or posted the 39-second video or where, though a U.S. official said it was a "reasonable conclusion" it was filmed in Afghanistan.
The official, based in Afghanistan, spoke on condition of anonymity because of the sensitivity of the issue.
President Barack Obama knows about the video, said White House spokesman Jay Carney, who said he didn't know if Obama had viewed it. "What it apparently depicts is deplorable, reprehensible and unacceptable," Carney said, adding the president agrees with Panetta's statement.
Amos said he has pulled together a team "to thoroughly investigate every aspect of the filmed event." He said he will also assign a Marine general officer and a senior attorney, both with combat experience, to conduct an internal preliminary inquiry into the matter.
"Once the investigation and preliminary inquiry are complete and the facts have been determined, then the Marine Corps will take the appropriate next steps," Amos said. "We remain fully committed to upholding the Geneva Convention, the laws of war and our own core values."
"We are aware of the video. The hate in it does not represent the U.S. Marine Corps," said Col. Ricco Player, a spokesman for the Marines in Afghanistan's volatile Helmand province.
Secretary of State Hillary Clinton expressed "total dismay at the story concerning our Marines who I have the highest respect and admiration for." She called the behavior "deplorable."
"It is absolutely inconsistent with American values, with the standards of behavior that we expect from our military personnel and the vast, vast majority of our military personnel, particularly our Marines, hold themselves to," she said. "Anyone found to have participated or known about it, having engaged in this kind of conduct, must be held fully accountable."
Afghan President Hamid Karzai called on the U.S. government to investigate the video and hand down the harshest punishment possible.
"The government of Afghanistan is deeply disturbed by a video that shows American soldiers desecrating dead bodies of three Afghans," according to a statement released by the presidential palace on behalf of Karzai.
"This act by American soldiers is simply inhuman and condemnable in the strongest possible terms."
A Taliban spokesman called the video "barbaric."
"And no religion that follows a holy text would accept such conduct. This inhuman act reveals their real face to the world," Taliban spokesman Qari Yousuf Ahmadi said via text message Thursday.
The U.S. Embassy in Kabul said in a statement Thursday it "strongly condemns" the actions in the video.
"Such actions are reprehensible, dishonor the sacrifices of our military and the American people and violate the core values of both our societies," the embassy said.
"Islam gives values and respect to every human being," regardless of which religion the individual follows, said Islamic scholar Mawlawi Enayatullah Baligh. "The value and respect is the same for an alive person and a dead body. Even the body of your enemy in the battleground is respectable in Islam."
The video surfaces at a critical time for relations among the United States, the Afghan government and the Taliban.
Last year, the United States outlined its plan to withdraw its troops from Afghanistan, beginning by pulling out 33,000 "surge" troops who had been deployed to help quell the violence by the end of 2012. The remaining 68,000 troops would be withdrawn by the end of 2014.
Meanwhile, the Taliban tentatively agreed in recent weeks to open an office in Qatar's capital city of Doha, a decision widely seen as an overture aimed at establishing an outside forum for political talks with NATO-led forces and the current Afghan administration, among others.
A senior Marine Corps official who has examined the video said Wednesday that the Marines are carrying 30-caliber sniper rifles and wearing helmets issued to members of Marine sniper teams. The helmets are designed with a shorter front and sides so that snipers can place rifles and scopes near their faces.
The official added that the desecration of a body by U.S. troops could be considered a potential war crime.
"We recently became aware of an inappropriate video on a public website that appears to involve members of our military," International Security Assistance Force spokesman Col. Gary Kolb said from Kabul. "We will not speculate on the details but will take all necessary actions to determine the facts."
"Regardless of the circumstances or who is in the video, this is egregious, disgusting behavior," said Department of Defense spokesman Capt. John Kirby. "It's hideous. It turned my stomach."
In a statement released Wednesday, the Washington-based Council on American-Islamic Relations condemned the video.
"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," wrote CAIR National Executive Director Nihad Awad in a letter to Panetta.
"Any guilty parties must be punished to the full extent allowed by the Uniform Code of Military Justice and by relevant American laws."
CNN's Nick Paton Walsh, Masoud Popalzai, Barbara Starr and Tom Cohen contributed to this story.