WASHINGTON — The Marine Corps on Friday laid the groundwork for deciding what, if any, disciplinary action will be taken in the case of an Internet video purporting to show Marine snipers urinating on dead bodies in Afghanistan.

The top Marine officer, Gen. James Amos, appointed three-star Gen. Thomas Waldhauser to oversee the case. Waldhauser named another officer to do an internal Marine Corps investigation, which is in addition to a criminal probe under way by the Naval Criminal Investigative Service.

Waldhauser will decide what to do as a result of the investigations.

In Afghanistan, a senior US commander issued a letter to all personnel in the international coalition that is fighting the war, explicitly reminding them of the need to respect the dead. The letter from Army Lt. Gen. Curtis M. Scaparrotti, commander of the International Security Assistance Force Joint Command, reflected the depth of concern about fallout from the video.

“Defiling, desecrating, mocking, photographing or filming for personal use insurgent dead constitutes a grave breach of the LOAC (laws of armed conflict), violate basic standards of human decency and can cause serious damage to relations with the Afghan government,” Scaparrotti wrote. He ordered all commanders to remind their subordinates of their duty to comply.

No one has been charged in the case, which triggered widespread outrage with the appearance Wednesday on YouTube of a brief video that appears to show four Marines in full combat gear urinating on the bodies of three dead men lying on the ground.

Marine Gen. John Allen, the top U.S. and NATO commander in Afghanistan, condemned the behavior and said in a statement Friday while he was traveling in the U.S. that the facts in the case should be determined swiftly.

“These actions are in direct opposition to everything the military stands for,” Allen said after viewing the video. “Such acts in no way reflect the high moral standards and values we expect of our armed forces on a daily basis.”

Pentagon officials worry that the actions depicted in the video will tarnish the reputation of the entire military. Some officials have expressed fear that it could undermine prospects for exploratory Afghan peace talks.

Defense Secretary Leon Panetta and military leaders have promised an exhaustive investigation and sought to contain the damage at home and abroad.

Marine Corps headquarters at the Pentagon issued a statement Friday announcing Amos’s appointment of Waldhauser, commander of Marine Forces Central Command, which is responsible for Afghanistan.

It said Waldhauser will “exercise his independent judgment” and decide how to handle “any allegations of wrongdoing.”

Waldhauser appointed a three-star general, Steven Hummer, to lead the internal Marine Corps investigation. The probe will look into the question of what prompted the four Marines’ behavior, said one officer, speaking on condition of anonymity in order to discuss an internal matter. That will include examining whether the Corps’ current training and education on the laws of warfare are adequate, the officer said.

A second officer, also speaking privately to discuss an internal matter, said investigators will consider whether more senior Marines, such as the commander of the four Marines’ battalion, failed to ensure a climate of proper discipline. The four who appeared in the video are enlisted Marines. Their exact ranks have not been made public.

The NCIS, the law enforcement arm of the Navy, is heading the main inquiry, which is expected to consider evidence of violations of the U.S. military legal code as well as the international laws of warfare.

By Friday, the NCIS had identified and interviewed all four of the Marines appearing in the video. At the time, they were filmed urinating on the bodies, the four were members of the 3rd Battalion, 2nd Marines, which fought in the southern Afghan province of Helmand for seven months before returning to their home base at Camp Lejeune, N.C., last September.

Two of the four, plus the commander of the battalion, had moved on to other assignments before the video appeared on the Internet, according to Marine Corps officials who spoke on condition of anonymity in order to discuss an active investigation. The Marines’ names have not been made public.

In its first public statement about the probe, the NCIS said Friday the probe is in its “very early stages.” NCIS communications director Maryann B. Cummings said all four Marines are in the U.S., but she provided no other details about them. She said investigators are looking for information about those who created the video and posted it on the Internet.

The video itself is being studied for clues with the use of NCIS “computer forensic techniques,” she said without elaborating.

The emergence of the Internet video didn’t seem to immediately set back movement toward exploratory negotiations with the Taliban. Asked about possible implications for peace talks, Secretary of State Hillary Rodham Clinton said Thursday that the U.S. remained strongly committed to supporting Afghan efforts.

Panetta, however, said the incident could endanger the talks.

“The danger is that this kind of video can be misused in many ways to undermine what we are trying to do in Afghanistan and the possibility of reconciliation,” Panetta said at Fort Bliss, Texas.

He said it was important for the U.S. to move quickly to “send a clear signal to the world that the U.S. will not tolerate this kind of behavior and that is not what the U.S. is all about.”