Rescue workers are still searching through the concrete rubble as some people are still feared trapped, they said.
A resident of the ill-fated building claimed that some commercial activity was being carried out on the ground floor of the building and that might be the reason of its collapse.
According to the fire brigade officials engaged in the rescue operation, 18 people have been pulled out of the debris so far and referred to the nearby hospitals.
The National Disaster Response Force (NDRF) has also been pressed into service to rescue those trapped under the rubble.
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The structure that came down this morning in the Ghatkopar's Damodar Park area housed around 15 families.
Most of those trapped in the debris are believed to be elderly and women.
The civic body's control room received a call at around 10.43 am about the accident, said a BMC official, adding fire engines, a rescue van and ambulances were rushed to the spot immediately.
"I came out of my building and found lot of dust and heard cries and noise of people seeking help. I saw parts of the building collapsing," an eyewitness living in the neighbourhood said.
According to a local resident, it was a 35-year-old building.
The city and its suburbs had received heavy rains over the last several days, though there had been some respite from it since yesterday with showers becoming intermittent.
The Mumbai police cordoned off the area while the traffic was blocked on the Lal Bhadur Shastri road to provide a 'green corridor' to rush the rescued to hospital.
Rajesh Diyora, a resident of the same building, said some commercial activity was being carried out on the ground floor of the building and that might be the reason for its collapse.
He said he escaped unhurt in the collapse as he had left for his office before the building collapsed.
The building was not listed in the dangerous category, as per locals.
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