NEW DELHI (AFP) - The Indian father who killed his daughter and beheaded her boyfriend after they eloped has declared he feels no remorse over the "honour killings", media reports said on Friday.

The young couple from India's northern state of Haryana were beaten to death on Wednesday by the father and other relatives of the 20-year-old woman "to protect the family and village honour", the police said.

After killing the man, 22, using sticks, the attackers beheaded him. They also tried to burn the woman's body but were stopped by the police.

The woman's family disapproved of the three-year relationship because the couple belonged to the same caste and were "considered brother and sister", the police said.

The father, who has since been taken into custody, showed no signs of remorse over the brutal killings as he spoke to local reporters in Haryana's Rohtak district.

The woman's mother and uncle have also been arrested over the killing, and the police said they were searching for a brother.

"I have done nothing wrong. I have cleaned up a social wrong," the father, Billu Pehlwan, a dog breeder by profession, was quoted as saying by the Times of India and other newspapers.

The NDTV network showed him saying: "I would do it again. I have no regrets."

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

The killings are carried out by close relatives or village elders to protect what is seen as the family's reputation and pride.

The dead woman was studying to be an art teacher while her boyfriend was a student at a local college.

They were on their way to the capital New Delhi, about 70km from Rohtak, when they were tracked down and hauled back to their village.