The condition of girl, who is admitted to AIIMS Trauma Centre, is said to be critical.
According to police, the incident took place on July 2 when victim, a resident of Munirka, was going to her typing classes.
"When girl was on way to her typing class, Pradeep Kumar stopped her and proposed her for friendship. However, she rejected his proposal which angered him and he started stabbing her in her abdomen, legs and neck and fled the spot," said a senior police officer.
Police said Pradeep went to the R K Puram police station soon after the incident and surrendered before the police, adding that he was staying in a rented accommodation in Mohammadpur village along with his friends.
He is a habitually offender and had been stalking the victim for the last six months, they said.