"The death toll in the collapse has risen to 13," a civic official told PTI, adding many more were believed to be trapped under the debris.
Four of the deceased have been identified as Lakhoji Devji Chawda (60), Jamuna Chawda (30) Anil Chawda (19) and Santosh (44).
The injured have been admitted to the state-run JJ Hospital and Nair Hospital.
Around 21 families, which were BMC's tenants, lived in the 30-year-old structure.
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The kin of the missing wailed as a heavy machinery lifted large slabs of concrete and rescue workers looked for the dead or survivors under the rubbles of the building.
The building is located on Brahmadev Khot Marg near Babu Genu market in the Mazgaon area, which is close to the Dockyard Road railway station on the harbour railway line.
Anish Kadam (10), Diptesh Kadam (16), Habib Shaikh (22), Tauqeer Shaikh (22), Haroon Shaikh (24) and Ajay Chendvankar (40) were among those rescued.
Maharashtra Chief Minister Prithviraj Chavan held a meeting with senior officials and asked them to ensure effective relief and rescue operation.
BMC said it has formed two committees to probe the collapse incident and ordered audit of similar buildings in the city.
The civic body has filed a complaint against one 'Mamamiyan Decorator' who had allegedly made some alterations on the ground floor of the building, civic officials said.
The affected families would be given alternative accommodation in the vicinity. It has also announced a compensation of Rs 2 lakh each to the family of the deceased.
This is the second major building collapse in Mumbai this year. Aftab Mansion, a residential building in suburban Mahim West had collapsed in June, killing ten people.