Kumar, a 1976-batch officer, who was serving as Tihar Jail Director General, succeeded B K Gupta, who retired from service after holding the post of Commissioner for the past 20 months since November, 2010.
The 59-year-old officer outlined anti-terror activities, prevention and detection of crime, maintenance of law and order and improving the perception of policemen among public as the challenges before him.
"We have arrested terrorists. But it is wrong to think that with these arrests, the city is now safe from terror attacks. It is a dynamic situation. We have to keep our vigil," he told reporters after taking over as the new chief.
He said the force will not be seen as wanting in dealing with the issues related to policing.
He also emphasised on the need for improving the interface of police with public. "It should improve. I won't say it is poor. There is a need for a better rapport. The complainants should know what is the follow up," he said.
As he arrived at the Delhi Police Headquarters, he was welcomed by senior officials and given a gun-salute. At the chambers, he signed the papers.
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Earlier in the day, Gupta was given a warm farewell where he said constables who stand under scorching sun for long hours while performing their duties are the "real heroes" and they should be treated with respect.
Gupta also said that he had a "very satisfying" tenure as the capital's police chief and claimed that street crime had come down after he took over.