Radio Free Europe hosts video obtained by Reuters:

Afghan authorities say an investigation has been launched in a bid to apprehend the Taliban militants responsible for the alleged public execution of a woman accused of adultery in northern Afghanistan.

International and Afghan outrage has been mounting over the alleged shooting death, which was captured in a video obtained by the Reuters news agency.

More from CNN:

Officials in Afghanistan, where the amateur video was filmed, 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, said Parwan province governor Abdul Basir Salangi.

"In order to save face," they accused her of adultery, Salangi said.

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.

"We went there to investigate and we are still looking for people who were involved in this brutal act," he said.

It is not clear from the video when it was filmed.

The killing took place in the village of Qimchok, not far north of the capital Kabul.

Several hundred activists marched in Kabul to protest the killing today:

Afghan activists quickly organized a march today in Kabul for several hundred women and men aimed at bringing attention to Najiba's killing, alleged to have come at the hands of the Taliban. Details surrounding the circumstances of the woman's murder at close range remain murky, but the story involves two commanders said to be involved with the young woman and a decision to settle the matter at gunpoint by killing her without any kind of trial for the crime of "adultery."

The leaders of Wednesday's march say they chose to speak out publicly in order to force their government to bring the men who committed the crime to justice.

"It is very important because the government is not taking us seriously at all," says Wazhma Frogh, a civil-society activist focused on women's rights. "With this march we are telling the government that we are not stoned to death, we are still alive, we are still standing."

Frogh and others say they face threats from some in the community who want them to stay home and keep quiet when it comes to the case. They also have been criticized by those who ask why they "don't march when the U.S. kills Afghans, only when mujahedin do?" But they decided to go ahead with the protest because they have received support from many quarters, including the Kabul police chief, members of Parliament, and the Ministry of the Interior.