Kabul, Afghanistan (CNN) -- Afghan President Hamid Karzai ordered the arrest Monday of the Taliban who participated in the public execution of a woman accused of adultery.
Shock and outrage have mounted since an amateur video surfaced of a burqa-clad woman sitting on the ground while a man standing a few feet away shoots her nine times before a cheering mob.
The execution raises questions about what the 2014 withdrawal of NATO troops from Afghanistan will mean for women, who regained basic rights of education and voting after the fall of the Taliban in 2001.
Karzai condemned the killing and ordered security officials to arrest and punish those involved, according to a statement released by the president's press office.
Officials in Afghanistan, where the amateur video was taken, believe the woman was executed because two Taliban commanders had a dispute over her, according to the governor of the province where the killing took place.
Both apparently had some kind of relationship with the woman, Parwan province Gov. Abdul Basir Salangi said.
To save face, they accused her of adultery, Salangi told CNN on Sunday. Then they "faked a court to decide about the fate of this woman and in one hour, they executed the woman," he added.
Both Taliban commanders were subsequently killed by a third Taliban commander, Salangi said.
Karzai called on officials to track down everyone involved, including those in the video.
"We went there to investigate, and we are still looking for people who were involved in this brutal act," he said Sunday.
U.S. Marine Gen. John Allen, commander of NATO-led forces in Afghanistan, said he was encouraged by reports that provincial police were "investigating the circumstances surrounding this atrocity."
He also offered the assistance of NATO troops to track down those responsible for the killing, according to a statement released by the U.S.-lead International Security Assistance Force.
The killing took place in the village of Qimchok in Shinwari district, just north of the capital of Kabul.
Karzai described those involved in the shooting death as "cowards," saying "such crimes are unforgivable both in Islam and under our country's laws," the statement from his press office said.
The United States condemned the killing "in the strongest possible terms," calling it a "cold-blooded murder."
"The protection of women's rights is critical around the world, but especially in Afghanistan, where such rights were ignored, attacked and eroded under Taliban rule," the American Embassy said in a statement Sunday.
The public execution is the latest and among the most shocking examples of violence against women in Afghanistan, but it is far from an isolated case.
Hundreds of students and teachers at girls' schools in the country have been hospitalized with suspected poisoning this year alone. Girls were forbidden to go to school when the Taliban ruled the country from 1996 to 2001.
Nearly nine out of 10 women suffer physical, sexual or psychological violence or forced marriage at least once in their lifetimes, Human Rights Watch said in its 2012 annual report.
CNN's Richard Allen Greene, Chelsea J. Carter and Sara Sidner, and journalist Ruhullah Khapalwak contributed to this report.