The incident took place at JNU's School of Languages at around 11 am which sent shock-waves among the students of the prestigious university.
The boy, identified as Aakash died a few hours later in the All India Institute of Medical Sciences (AIIMS) trauma centre while the girl, identified as Roshni (22), is battling for life in Safdarjung Hospital, police said.
They said Akash had an argument with Roshni following which he attacked her with an axe, inflicting serious injuries including on the head.
Police claimed it to be a case of one-sided love.
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They have recovered a knife, a Salphas bottle and the axe used in the crime. A country-made pistol was also recovered from the spot.
Later in the day, Roshni was operated upon and was shifted to the intensive care unit (ICU) of the Safdarjung hospital.
She is on ventilator and her condition is critical. She had suffered severe head injury with "depressed fracture", they said adding the doctors operated upon her and removed the fractured fragments and her condition is being constantly monitored.
In a statement, the JNU administration condemned the incident and said every possible step is being taken to ensure that such incidents are not repeated.
"A preliminary fact finding committee consisting of six members has been formed to investigate into the incident. The Vice Chancellor also held a meeting with various deans of the university to discuss the matter, said Poonam S Kudaisya, JNU's Public Relations Officer.
Shocked students at the university have demanded better security. "It is a very shocking incident. We need better security," said a JNU student.