The letter came a day after Kejriwal posted an audio clip on social media asking people not to remain "mute spectators" to violence against women and take action to stop such incidents.
The AAP government also came out with an advertisement on radio channels with the audio clip.
Taking strong objection to the letter, BJP asked Kejriwal to stay within his "limits" while coming down hard on him for repeated barbs at the Prime Minister.
"I have a small, humble request. Either you spare at least one hour a week to Delhi's law and order situation, fix accountability for the Delhi Police and interact with the people of Delhi - or give us the control of Delhi Police. With the help of people, we will improve functioing of Delhi Police," said Kejriwal
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In the letter, Kejriwal said the city government does not have any control over Delhi police and that it comes under the Prime Minister as per law. "And you are not being able to give it time as you are the Prime Minister of the country and you have to take care of the whole country."
The face-off between Delhi Police and AAP government intensified today with both sides hardening their positions following a meeting between city's top police officer B S Bassi and Kejriwal held in the backdrop of the murder of the girl.
Delhi Police Commissioner B S Bassi had yesterday called on Kejriwal but the meeting appeared to widen the rift between AAP government and police and the top cop did not heed to most of the suggestions by the Chief Minister.