By Ben Farmer
The girl, Geesa, was attacked earlier this week by two men from the spurned family as she went to collect water from a stream in her village in northern Afghanistan.
The attack came after her father, Mohammad Rahim, had turned down a marriage offer for the girl, saying she was too young to be engaged.
"At this stage it looks like they wanted to marry her and the father refused, so they killed her," said Syed Sarwar Hosseini, police spokesman for Kunduz province.
Two men, named as Massoud and Sadeq, have been arrested on suspicion of the murder, in Kulkul village of Imam Sahib district, he said. The two men were relatives of Geesa and lived in the same village.
The provincial director of women's affairs said the province had been hit by a wave of violence against women.
Nadira Giah said 11 girls and women had been killed this year, up fivefold from last year.
In January, a young woman was reportedly murdered in the province by her husband and her mother-in-law for giving birth to a daughter. The 22-year-old woman called Stori was strangled after giving birth to a third daughter, when her husband wanted a son.