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British Foreign Secretary William Hague osaid he was “shocked and disgusted” by reports of the execution.
The British Government condemned the “deplorable” action and called upon Afghanistan's rulers to bring the perpetrators to justice.
“I am shocked and disgusted by (the) reports,” Mr Hague said in a statement. “Such deplorable actions underline the vital need for better protection of the rights of women and girls in Afghanistan.”
The 22-year-old woman from a village in Parwan province, north of the Afghan capital where there is little government control, was reportedly accused of adultery.
“A 22-year old woman was shot in the head by the Taliban insurgents one week ago in Shinwari district of Parwan province,” a local government official who asked not to be named said on Sunday.
Parwan has recently seen a rise in violence, with Taliban insurgents taking over villages in at least two districts.
“The villagers from where she was killed gave us a 37-second video, which shows the woman sitting in a field and about 100 villagers are there to watch her execution,” the official said.
The video shows her being shot repeatedly in the back.
The villagers say a local Taliban commander had an illegitimate relationship with the woman and that his colleagues killed her to save his reputation.
The woman, named as Najiba, was married to a member of a hardline Taliban militant group and was accused of adultery with a Taliban commander, Parwan provincial spokeswoman Roshna Khalid said.
The Taliban have rejected any involvement, saying the woman was possibly killed due to personal hostilities.
“I investigated and found out that the Mujahideen (freedom fighters) had no hands in this case and the woman was killed by her villagers. Almost everyone is armed in rural areas,” Taliban spokesman Zabihullah Mujahid said.
Afghan human rights campaigners have asked the government to bring those responsible to justice.
“This shows that women are still the first victims of violence in Afghanistan, despite efforts being done to reduce it,” Musa Mahmoudi of the Afghan Independent Human Rights Commission said.