Of the 11 bodies recovered, four at Royapettah Govenment Hospital are yet to be identified, police said.
Six persons have so far been arrested in connection with the tragedy, they said.
The Chief Minister who earlier in the day announced a solatium of Rs 2 lakh for families of those killed and Rs 50,000 for the injured, said 31 people have been recovered so far, of whom 11 had died and 20 were being treated.
The Chief Minister consoled the injured patients and handed each of them the solatium amount.
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Asked for the reason behind the incident, she said, "It appears that the builders did not adhere to the approved plan. The building appears to have serious structural defects. Tests have to be conducted to see whether the soil is capable of bearing such a building."
"We have made arrangements to house and feed families of the workers who are trapped inside. The government has made all arrangements for their housing, shelter and food. We will look after them until everything is over. Meanwhile, rescue efforts are continuing unabated. We hope that we will save as many lives as possible," Jayalalithaa said.
Earlier, she visited the accident site at Mugalivakkam where the 11 storeyed high rise came down last evening, and inspected the rescue operations underway.
Tamil Nadu Chief Secretary Mohan Verghese Chunkath, Director General of Police K Ramanujam, State Disaster Management Authority Commissioner T S Sridhar, Chennai Police Commissioner S George and senior officials were present during the CM's visit to the spot.