Five people, including a family with two young children, were still missing by early evening, according to a local official.
Media reports said neighbours heard no explosion -- just the crash when the building collapsed.
Witnesses said a freight train passed on the neighbouring railway track just before the building collapsed, while others noted that renovation works had been under way on the lower floors.
Prosecutors in Torre Annunziata have opened an investigation to determine what caused the accident.
Media reported that the bodies found were those of a local technician, his wife and their 25-year-old son.
Some 30 firefighters, joined by dozens of volunteers and relatives of the missing using their bare hands, searched the wreckage for survivors in the scorching heat.
The fire service said three officers had been lightly injured during search operations.
"It is clear that this building was in bad shape," local mayor Vincenzo Ascione said. "I regret that no city technician had been able to recognise the situation because there had to have been a sign".
Those still missing are a couple and their children aged eight and 11 and a 65-year-old woman who lived alone, Ascione said.
Authorities said electric generators as well as spotlights would be brought to the scene to facilitate the search, which was expected to go on until late evening.
The rescuers continued to stop regularly, hoping to hear calls for help.
Sniffer dogs were also on site to help locate the missing.
Train traffic on the adjacent railway track was halted as a safety precaution.