At least 17 people, including three firefighters were injured, Mamdani said on Thursday as rescue operations continued.
The city's fire department earlier said four people were in critical condition after the three-storey building in the Flatbush area of Brooklyn collapsed about 4pm on Wednesday and tumbled into the adjoining construction site where excavation work was ongoing.
New York television station WABC-TV reported that at least four survivors were pulled from the wreckage about two and a half hours after the collapse, including a pregnant woman.
The number of people who were at home when the 1930-era building collapsed was not immediately known, officials said.
They did not say how many workers were on the construction site at the time.
City Fire Department Commissioner Lillian Bonsignore said seven children were among those affected by the collapse.
She declined to say whether any of the dead were children or adults.
Mamdani said the city's Department of Buildings and law enforcement officials were investigating the cause of the collapse.
A firefighting crew that happened to be in the neighbourhood was on the scene within a minute of the collapse and helped pull the first victims from the debris, authorities told reporters at an evening press conference on Wednesday.
Local television news footage showed rescue workers with search dogs combing through the building's ruins, removing debris in buckets to look for any signs of people who may have been trapped in voids beneath the debris.
John Esposito, the city's fire department chief, said it would take rescue teams several days for the entire site to be "searched for all potential victims," adding, "We do not know how many people are missing overall."
About 250 fire and emergency medical services personnel were deployed to the scene, the fire department said.
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