The three-story building caved in Monday, killing six people at the scene and injuring 11 others, the Press Trust of News agency reported. Four of the injured died Tuesday in local hospitals, the report said.
Pune is in western Maharashtra state, of which Mumbai is the capital.
The report, quoting sources, said most of the victims were construction workers who had been staying at the site.
Police have arrested two people, who had ownership of the land where the building was coming up, and filed charges against them, the report said.
Officials said the building was an unauthorized construction and notices had been issued earlier to the two arrested men.
The Times of India said they faced charges of culpable homicide not amounting to murder and causing hurt and endangering the lives of others.