The US military is investigating the video’s authenticity, and origin, which is not yet known.
The footage shows four men in military fatigues appearing to urinate on the bloodied corpses of men. They have brown skin, bare feet and are dressed in loose-fitting outfits. One appears to be covered in blood.
A man’s voice is heard saying: “Have a great day, buddy.”
The men in military fatigues seem to be aware they are being filmed.
In a statement, Karzai’s office said: “The government of Afghanistan is deeply disturbed by a video that shows American soldiers desecrating dead bodies of three Afghans.
“This act by American soldiers is simply inhuman and condemnable in the strongest possible terms. We expressly ask the US government to urgently investigate the video and apply the most severe punishment to anyone found guilty in this crime.”
Taliban spokesman Qari Yousuf Ahmadi told the BBC this “wild action” was not unprecedented, and that Taliban attacks on Americans in Afghanistan would continue.
However, another Taliban spokesman, Zabihullah Mujahid, said the video “is not a political process, so the video will not harm our talks and prisoner exchange because they are at the preliminary stage”.
Karzai said the video would not derail peace between the Afghan government and its Western allies.
As a step towards peace, Washington has been considering releasing several Taliban prisoners from the Guantanamo Bay.
The video has not yet circulated widely in Afghanistan, but once it does, the backlash may manifest on any foreign presence in Afghanistan.
“The US soldiers who urinated on dead bodies of Muslims have committed a crime,” Kabul resident Feda Mohammad told Reuters news agency.
“Since they’ve committed such a crime, we don’t want them on our soil anymore.”
The US Marine Corps has condemned the video, and said the actions of the soldiers were not consistent with its core values.
In a separate case, the US military has been prosecuting five soldiers from the army’s 5th Stryker Brigade who are accused of killing Afghan civilians during their deployment in Kandahar province in 2010.
The US has about 20,000 Marines deployed in Afghanistan, based mostly in Kandahar and Helmand provinces. In total, about 90,000 US troops are on the ground in Afghanistan.
The US and its partners in Afghanistan have said they plan to hand over security of the country and withdraw combat troops by the end of 2014.
Watch the video here: