The youngest person who died in the fire was a one-year-old, police said. The oldest was 97.
Police said they have completed a search for bodies inside all seven of the eight high-rise residential towers ravaged in the fire that first broke out a week ago and took more than 40 hours to be extinguished.
About 30 people were still reported missing.
"We have not finished our work yet," Commissioner of Police Joe Chow told reporters, adding that officials found suspected human bones in different apartments and would attempt DNA testing to identify them.
Officials will also continue to search through piles of fallen bamboo scaffolding to check if any remains or bodies were buried there, he said.
The deadly blaze broke out at Wang Fuk Court, in the northern suburban district of Tai Po, which was undergoing a months-long renovation project with buildings covered by bamboo scaffolding and green netting.
The city's anti-corruption body and police said they had arrested 15 people, including directors at construction companies, as authorities probe corruption and negligence in relation to the renovation work.
Police said six others, from a fire service installation contractor, were arrested.
They were believed to have deactivated some fire alarms at the housing complex during the renovation works, according to police, and were suspected of making false statements to the fire services department.
Residents at Wang Fuk Court and officials have previously said some fire alarms in the buildings failed to sound when the blaze broke out, though it was not immediately clear how widespread that problem was within the complex.
Authorities also pointed to substandard plastic nylon netting covering scaffoldings erected outside the towers at Wang Fuk Court, and foam boards installed on windows, for contributing to the fire's rapid spread to seven of the eight buildings at the complex.
On Wednesday, government officials ordered the removal of all external scaffolding nets from up to hundreds of buildings across the city that are undergoing major renovation or maintenance work. The materials will need to be tested before they are allowed to be installed again.
The removal was triggered by initial findings at two housing complexes in the territory where fire safety inspection reports for scaffolding nets were suspected to have been falsified, said Chris Tang, Hong Kong's Secretary for Security.
Police are investigating the companies that they believe could have provided the test reports, including the Binzhou Inspection and Testing Center in China.
The initial cause of the fire was still under investigation.
Nineteen bodies among the 159 were still unidentified, police said.
Ten migrants who worked as domestic helpers at the housing complex, including nine from Indonesia and one from the Philippines, as well as one firefighter, were among those killed.
