A spokesman for the Municipal Corporation of Greater Mumbai told CNN that the building was 117 years old and had been deemed unsafe years ago.
“The building was served an ‘unsafe to live’ notice in 2013,” said the spokesman, Vijay Khabale-Patil.
“Ten families used to live in the building and some of them had vacated the property recently. So we don’t have an actual count of the missing people.”
He told CNN that 13 bodies had been recovered from the site and the operation was still “in full swing.”
Twenty others were rescued and sent to hospital, according to Deven Bharti, the joint commissioner for law and order of the Mumbai Police.
“We are still assessing how many people might have been trapped,” Mumbai police spokesman Rashmi Karandikar told CNN.
The building collapse comes after heavy rains and flooding in Mumbai this week, which have killed at least five people. Authorities would not say if the collapse was connected to the rainfall.
South Asia has seen a historic amount of rain and flooding this month, the height of monsoon season.
More than 1,200 people have been killed in India and Bangladesh and some 41 million have been affected by flooding, according to the International Federation of Red Cross and Red Crescent Societies. Nepal has also been hit hard.
Thursday’s building collapse is the second significant one to hit India’s financial hub this summer. More than a dozen people were killed when a five-story building collapsed in the Ghatkopar neighborhood in July.
In May, a wall collapsed at a wedding, killing 24 people.
Deadly infrastructure accidents are not unusual in India. Critics say construction projects often lack proper oversight and safety controls.