The deceased girl had allegedly fled from Balasore district and stayed with her lover Nigamananda Mallick (28) at Balakati, on outskrits of the state capital.
Both the girl and Nigamananda ran away from their houses after the girl's parents disapproved of their marriage, police said.
The arrested parents, identified as Radhagobinda Mallick and Shantilata Mallick, then went to Balakati last night where the duo were staying.
"They persuaded the daughter to come back to the village where they promised to organise their marriage," police said.
Though the parents were yet to confess the crimes, DCP Nitinjit Singh said, "It appears to be a case of honour killing.
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