"I don't believe in quitting. I am not a quitter," Mr Kumar told a TV channel.
He made the remark amid demands during the protests by students and the youth in New Delhi that he resign owning moral responsibility for alleged lapses by police that led to the gang-rape of the 23-year-old physiotherapy student in a moving bus last Sunday night.
Mr Kumar said he will continue in his job as long as he is asked to.
Asked whether he had any regret over the police action in dealing with the protesters at India Gate today, Mr Kumar said every situation could be handled better.
"Maybe there were some lapses here and there. But by and large, the situation warranted this kind of action," he added.
Police had to resort to lathicharge and use of teargas and water cannons to disperse the agitators after the protests turned violent.