A graphic video of the stoning shows the woman, named as Rokhsahana, aged between 19 and 21, in a hole in the ground as men almost casually hurl stones at her with sickening thuds.
Rokhsahana was heard repeating the shahada, or Muslim profession of faith, her voice growing increasingly high-pitched in the nearly 30-second clip run in Afghan media. Local authorities confirmed the footage.
The killing took place about a week ago in Ghalmeen, an area some 40 kilometres (25 miles) from the Ghor provincial capital of Firozkoh, governor Seema Joyenda said.
Rokhsahana had been "stoned to death by Taliban, local religious leaders and irresponsible armed warlords," Ms Joyenda told AFP.
Seema Joyenda, one of Afghanistan's only two female governors, said that according to authorities' information Rokhsahana's family had "married her to someone against her will and she was eloping with a man her age".
She condemned the stoning, calling on Kabul to take action to "clean the area".
"This is the first incident in this area but will not be the last. Women in general have problems all over the country, but especially in Ghor... The man with whom she was eloping has not been stoned."
Ghor police chief Mustafa Mohseni told AFP that the incident happened in a Taliban-controlled area, confirming that it was the first such incident "this year".
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