A senior US military official said the Marines believed they had identified the unit at the center of the allegations, which evoked memories of previous abuses committed by US troops in Iraq and during the decade-long Afghan war.
"We cannot release the name of the unit at this time since the incident is being investigated," a spokesman from the Marines said, referring to images that could spark outrage and unrest in Afghanistan and the wider Muslim world.
US cable network CNN quoted an unnamed US Marine official as saying the military branch was "confident" the troops in the inflammatory video were from the 3rd Battalion 2nd Marine Regiment, based at Camp Lejeune, North Carolina.
The unit deployed to Afghanistan, mainly in Helmand province, in early 2011 and returned in September or October, CNN reported.
The video appeared to show four servicemen urinating on three bloodied corpses, and one of the men, apparently aware he was being filmed, saying: "Have a great day, buddy," referring to one of the dead.
US Defense Secretary Leon Panetta pledged that "those found to have engaged in such conduct will be held accountable to the fullest extent," and a Pentagon spokesman confirmed a probe into the alleged abuse was under way.
"This conduct is entirely inappropriate for members of the United States military and does not reflect the standards or values our armed forces are sworn to uphold," Panetta said in a statement.
"I have seen the footage, and I find the behavior depicted in it utterly deplorable. I condemn it in the strongest possible terms."
US Secretary of State Hillary Clinton told reporters of her "total dismay at the story concerning our Marines," and joined Panetta in condemning "the deplorable behavior that is reflected in this video."
"It is absolutely inconsistent with American values, with the standards of behavior that we expect from our military personnel," Clinton said.
The Taliban, who have made recent moves toward talks to end 10 years of US-led war in the impoverished country, described the apparent abuse as "an inhumane and savage act by the American soldiers in Afghanistan."
But spokesman Zabihullah Mujahed said he did not think it would destroy tentative peace negotiations with the United States, "which at this stage are mainly about prisoner exchange".
Earlier in the day, the insurgents issued another statement supporting talks to end the war against US-led forces, while warning that this did not mean surrender.
The Pentagon says it has not yet verified the footage, which has been broadcast by leading Afghan television station Tolo News and posted on the Live Leak website.
Afghan President Hamid Karzai said in a statement that the government of Afghanistan was "deeply disturbed" at the desecration.
"This act by American soldiers is simply inhuman and condemnable in the strongest possible terms," he said, requesting that the US urgently investigate and "apply the most severe punishment" to anyone found guilty.
On the subject of peace talks, the Taliban, who have announced their readiness to open a political office in Qatar, said they had increased their "political efforts to come to mutual understanding with the world."
"But this understanding does not mean a surrender from jihad and neither is it connected to an acceptance of the constitution of the stooge Kabul administration," the hardline Islamists said in a statement received by AFP.
"But rather the Islamic Emirate (the Taliban) is utilizing its political wing alongside its military presence and jihad in order to realize the national and Islamic aspirations of the nation and its martyrs."
The United States earlier announced that it would send a senior official to meet Karzai next week to see if he will agree to a resumption of preliminary talks with the Taliban. A US official said the talks could open within weeks.
A key Washington demand for any progress in negotiations is that the Taliban accept the Afghan constitution, which mandates protection for the rights of women and minorities, which were stifled during Taliban rule from 1996 to 2001.
Another crucial element would be a renunciation of violence by the Taliban and a break with Al-Qaeda and other "terrorist" groups, the US says.
