Of the 11 bodies recovered, four at Royapettah government 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.
"So far 31 people have been recovered. Out of them 11 are no more, 20 are receiving the best medical care and treatment in the hospital. Many of these workers are from Andhra Pradesh, some from northern states and efforts are on to locate the remaining workers. About 72 persons were working inside the building when it collapsed," she told reporters at a private hospital, where she met the injured.
The Chief Minister consoled the injured patients and handed each of them the solatium amount.
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."
Of those working inside, it appeared about 20 were women, she said.
"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.
Collectors of Vizianagaram and Nellore were also present.
Meanwhile, an official release from Chennai Police said "preliminary investigation revealed there was no coordination between the architects, structural engineers and site engineers over execution of the residential project developed by Prime Srishti Housing Private Limited".
The investigation also revealed that the structural engineer did not supervise the execution of the project periodically and that the builder did not follow norms prescribed by the structural engineer, it said.
"It also appeared that the builder executed the project under the supervision of inexperienced site engineers and the Managing Director alone supervised the execution, who does not have any technical knowledge," the release added.
Rescue personnel are continuing work, even during intermittent rains.
"Clearing the debris is a big challenge, it will take two to three days, going by our earlier experiences," National Disaster Response Force DIG S P Selvan said.
NDRF personnel were using advanced equipment to detect trapped people, he said, adding, 10 teams of NDRF are already on the job.
Meanwhile, a control room has been started in Vizianagaram by Collector Kantilal Dande in Andhra Pradesh following the mishap, as many of the labourers working in the building are reportedly from the district.
At least 14 people hailing from Vizianagaram were believed to be working in the building when it collapsed.
Six persons, including two owners and two engineers, who were arrested under various sections of the IPC were produced before a Magistrate in Sriperumbudur and sent to prison.
Massive rescue operations are on at the building collapse site at Mugalivakkam, with hundreds of personnel removing concrete debris using construction equipment, as several persons are believed to be still trapped.
According to a senior NDRF official this is the largest such building accident in the recent past in south India.
Sniffer dogs from Tamil Nadu Fire and Rescue Services are at the spot to locate those trapped in the rubble.
Minister of State for Heavy Industries Pon Radhakrishnan, MDMK leader Vaiko and MMK chief M H Jawahirullah, who visited the spot this morning demanded that those responsible be brought to book. DMDK leader Vijayakanth in a statement too condemned the incident and demanded action against those responsible.
The incident occurred around 5.30 pm yesterday.