Police officials said they were investigating the murder of Dharmender, 23, and Nidhi, 20, of Kalanaur village in Rohtak district, 70 km from New Delhi, whose bodies were found in the evening.
While the body of the Dharmender, with its head severed, was thrown outside his house, the woman was cremated by her family in a hush-hush manner, police said.
The two were good friends and studied together in a college in Rohtak. They were missing since Tuesday, sparking rumours of their marriage, police said.
Police officials said that families of both the victims have fled from their homes and raids are being conducted to find them.
As per the diktat of Khap panchayats (community councils), marriages within the same village and community are not allowed.