The remarks by a bench of Justices Siddharth Mridul and Najmi Waziri came while it was hearing a plea initiated by it on an alleged assault on the Dean and professors of the Delhi University's Law Faculty by some students last year.
The bench said "a sense of security" was missing on the campus of Delhi University (DU), especially among women and students, and directed the police to ensure that people felt safe there.
The police should also ensure that its staff does not tell victims of such an incident to "live with it" or that "it happens".
"We are not interested in how you do it. We are interested in the results, that women and others feel secure while moving around the campus. The Constitution empowers you (police) to ensure the safety of the people. We don't need to tell you what the Constitution says. So just do it," the bench said.
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The court told the police that certain crimes such as molestation and eve-teasing were "endemic" and these could be prevented if the agency knew where such offences were rife.
It said lack of immediate action by the police was the reason why people took to such crimes and this had to change.
The bench appointed an amicus curiae to assist it in determining the causes of such "unsavoury incidents", the "systemic failure" as well as "the complicity of the officials of the Delhi police and DU".
The court asked the police to expedite its probe in the matter and file an affidavit before the next date of hearing on September 26.
Law Faculty Dean Ved Kumari had earlier told the court that during the alleged violence against her and other professors, police officers present there were like "silent spectators" and did not lodge an FIR on the grounds that no complaint was received.
The first alleged incident of violence took place on May 19 last year when Law Faculty students were protesting at not being allowed to sit for semester examinations because of a shortage of attendance.
Similar incidents of unruly behaviour had occurred in November and December last year.