AAP leader Devendra Sehrawat alleged that Rana had written a letter to Lt Governor Najeeb Jung about the issue.
The party also claimed that a 70-year-old man died due to cold.
"This demolition has been carried out at the request of SP Rana to achieve the aim of polarisation in the residents of the area, copy of the letter (written by Rana to Jung) is also attached.
He demanded immediate relief to those whose jhuggies have been demolished.
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"One individual, 70 year old Noor Mohammad, died today morning before the morning Azan. Small children and women are being exposed to the cold and all this is happening while government agencies strive to provide night shelters to the needy poor.
"At this juncture it is important to take stock and provide immediate relief to them to prevent further loss of lives and at the same time initiate measures to ensure that the situation does not arise in the future," Sehrawat, who was the party's Lok Sabha candidate from South Delhi, said.