The seven-storey block in Thane collapsed late on Thursday, with more than 100 people reportedly inside.
Building work was going on even though four floors were already occupied. At least 70 people were injured.
Indian authorities said the block was one of many illegal high-rises in the Mumbai region, where demand for housing is driven by rapid population growth.
An investigation has been ordered, while a deputy municipal commissioner and senior police officer have been suspended for dereliction of duty and allegedly colluding with the builders.
Police were seeking the arrest of the builders, local police commissioner KP Raghuvanshi said.
At least 19 children are among the 72 people confirmed to have died in the collapse.
Rescue workers used heavy equipment on Friday and through the night into Saturday to try to cut through the rubble, while rescue dogs searched for survivors.
More than 100 people are reported to have been pulled out alive, among them a 10-month-old girl. But the Associated Press reported that her parents had not been found.
Hopes are fading of finding anyone else alive.
“The building collapsed like a pack of cards within three to four seconds,” Reuters quoted a local resident named Ramlal as saying.
“It just tilted a bit and collapsed.”
According to a police official, the collapse appeared to have been caused by the use of substandard building material.
Witnesses said the construction of the building started just six weeks ago, since when seven floors had been built. The eighth floor was under construction.
One local resident told the Associated Press the building was only supposed to have four storeys.
“People from the municipality used to visit the building but the builder still continued to add floors,” said the man, who did not give his name.
Building collapses are common in India, with poor construction practices often blamed.
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