"If my resigning will prevent (such crimes), then I am prepared to resign a thousand times. But that is not going to address the problem," he told the media.
He said the factors responsible for the rising crimes against women in the city were mental depravity, psychopathy and mental sickness.
"And that won't be sorted out by anyone resigning, least of all the leader of the police force," he said.
Earlier, asked if he would quit, Kumar shot back: "For any misreporting that you do, does your editor resign?
"If you do wrong reporting, does your editor resign? This is my counter question."