A man was beheaded and his girlfriend beaten to death in an "honour killing" in northern India after they eloped, police said Thursday.

The woman's mother, father and uncle were arrested after the gruesome murders carried out in a village in the state of Haryana on Wednesday, police said.

The couple were tracked down and brought back to their village in Rohtak district after they fled to the capital New Delhi, local police chief Anil Kumar said.

The woman, 20, was allegedly beaten to death and then relatives, angry about their decision to leave, turned on her 22-year-old boyfriend, attacking him with sticks, Inspector-General Kumar told AFP.

"While murdering the boy they also beheaded him," Kumar said.

The family had tried to burn the woman's body but were stopped by police, Kumar told AFP by telephone.

The pair had been in a relationship for three years. The woman was studying to be an art teacher while her boyfriend was also a student at a local college, Kumar said.

"We have arrested her father, mother and uncle and we are looking for her brother, a friend and driver of the car in which the couple were brought back to her home in Gharnavati village," the police chief said.

"Both belonged to the same village and the same caste.

"It is an honour killing but the murder was not approved by society."

India has for centuries seen killings that often target young couples who have relationships of which their families, clans or communities, particularly in traditional rural areas, disapprove.

Reasons for disapproval are numerous, but they sometimes include having relationships outside of their caste or religion.

The killings are carried out by relatives to protect the family's reputation and pride.

Police in Haryana have been conducting a campaign against honour killings in the state, where the sex-gender ratio is skewed in favour of men because of an outlawed but still existing tradition of female infanticide.

"We hold seminars and our women officers visit villages but the ultimate weapon against the scourge of honour killings is (more) education," Kumar said.

India's Supreme Court said in 2010 that the death penalty should be given to those found guilty of honour killings, calling the crime a barbaric "slur" on the nation.

There are no official figures on honour killings in India, but the All India Democratic Women's Association says its research shows about 1,000 such cases nationwide a year.

Also on HuffPost:

Loading Slideshow...
  • An Indian girl stands dressed as Lady Justice, as others shout slogans seeking death sentence for the juvenile convict who was earlier given a three year term in a reform home, after a judge pronounced death sentence for four others convicted in the rape and murder of a student on a moving New Delhi bus last year, in New Delhi, India, Friday, Sept. 13, 2013. (AP Photo/Altaf Qadri)

  • An unidentified lawyer from the prosecution side displays a victory sign as he speaks to journalists after a judge pronounced death sentence for all four men convicted in the rape and murder of a student on a moving New Delhi bus last year, in New Delhi, India, Friday, Sept. 13, 2013. (AP Photo/Saurabh Das)

  • Defense lawyer A.P. Singh speaks to the media after a judge pronounced death sentences for all four men convicted in the rape and murder of a student on a moving New Delhi bus last year, in New Delhi, India, Friday, Sept. 13, 2013. (AP Photo/Altaf Qadri)

  • An Indian woman lights a candle to mark the verdict after a judge pronounced death sentences for four men convicted in the rape and murder of a student on a moving bus in New Delhi last year, in Gauhati, India, Friday, Sept. 13, 2013. (AP Photo/Anupam Nath)

  • Defense lawyer A.P. Singh rubs his eyes as he comes out to speak to journalists after a judge pronounced death sentence for all four men convicted in the rape and murder of a student on a moving New Delhi bus last year, in New Delhi, India, Friday, Sept. 13, 2013. (AP Photo/Saurabh Das)

  • An Indian woman lights a candle to mark the verdict after a judge pronounced death sentences for four men convicted in the rape and murder of a student on a moving bus in New Delhi last year, in Gauhati, India, Friday, Sept. 13, 2013. (AP Photo/Anupam Nath)

  • Indian people light candles to mark the verdict after a judge pronounced death sentences for four men convicted in the rape and murder of a student on a moving bus in New Delhi last year, in Gauhati, India, Friday, Sept. 13, 2013. (AP Photo/Anupam Nath)

  • Indian people light candles to mark the verdict after a judge pronounced death sentences for four men convicted in the rape and murder of a student on a moving bus in New Delhi last year, in Gauhati, India, Friday, Sept. 13, 2013. (AP Photo/Anupam Nath)