Police rushed the duo to a hospital first from where they have now been shifted to a private hospital in Mysore, where they are stated to be "out of danger", they said.
The duo, aged 25 and 20, both daily wagers and belonging to 'Beda' community (a scheduled tribe), were in love and wanted to get married.
However, local gram panchayat member Chandru reportedly close to Congress MLA Chikkanna, was opposed to the alliance and allegedly pressured the 20-year-old girl's parents not to accept the boy as he supported a different political group.
The girl's father then beat her up and warned her not to meet her lover again. The two then eloped yesterday resulting in the girl's father allegedly committing suicide by hanging at his residence. Following this, Chandru allegedly threatened the boy that he would get him arrested.
Scared, the duo allegedly attempted to take their lives, police said.
"We are investigating the case from all angles," Superintendent of Police, Mysore District R Dilip said.
