The eight-storey building, which is located in the Kartal district on the Asian side of the city, collapsed on Wednesday but the cause is not yet clear.
Rescuers had initially put the death toll at two, but Istanbul governor Ali Yerlikaya said on Thursday the figure had leapt to 10 as more bodies were pulled from the rubble, state-run Anadolu news agency reported.
Another 13 people were injured, three of them seriously, he said.
As rescuers worked through the mountain of shattered concrete and twisted metal, which also crushed several nearby vehicles, they found a survivor on Thursday, a five-year-old girl.
She was taken to hospital but her condition was not immediately clear.
Rescue workers carry 5-year old girl Havva Tekgoz, after she was pulled from the rubble of an eight-storey building, some 18-hours after it collapsed. Source: AP
It was not immediately clear how many people were in the building when it collapsed, although 43 people were registered as living there in 14 separate apartments, Anadolu said.
Surveillance camera footage of the moment of collapse which was shown on Turkish television showed people fleeing in terror as the building disintegrated, leaving a huge cloud of dust.
Media reports said three of the eight floors had been illegally built in what is a relatively common practice in this metropolis of some 15 million.
Speaking to NTV news channel, several survivors said the building, which was riddled with cracks, had seemed to sway earlier in the day.
The incident was a stark reminder of the fragility of parts of Istanbul's residential infrastructure, with several buildings collapsing in recent years.
One four-storey structure crumbled last year following violent thunderstorms and in January 2017, two people died when another building collapsed in a working class part of town.
