The arrests were made on suspicion of manslaughter as investigators work to piece together what led to the catastrophic fire taking hold so fast in a complex of high-rise apartments.
Officials have been looking at factors including the styrofoam panels and bamboo scaffolding use in a renovation project at the site.
Officials also announced Monday that some of the exterior netting used on scaffolding at the housing estate did not meet fire-resistance standards.
Police representative Tsang Shuk-yin on Monday told a news conference that as of 4 pm (0800 GMT) the fire killed 151 people, up from Sunday’s toll of 146.
“We cannot rule out the possibility of this number increasing further,” Tsang said.
The blaze that engulfed Wang Fuk Court in Hong Kong’s northern Tai Po district was the world’s deadliest residential building fire since 1980.
Police have completed searches in five of the estate’s eight high-rise blocks.
Tsang said that “some remains have already been reduced to ashes” and that it was possible that some of the people reported missing will not be recovered.
Police found the remains have been found inside apartment units, in hallways, and on staircases, and will continue to search the buildings, he said.
Thirteen people have been arrested for manslaughter in relation to the blaze, Chan Tung, director of crime and security of the Hong Kong Police Force, told another news conference.
The group included 12 men and one women aged between 40 and 77.
Local media have reported that police have separately arrested three people for sedition, including 24-year-old student Miles Kwan, who had handed out flyers demanding government accountability over the fire.
Asked about the sedition arrests, Hong Kong security chief Chris Tang said there had been “inaccurate comments online” with the sole purpose of “threatening national security”.
“Therefore, we must take appropriate measures, including law enforcement measures. Operational details cannot be disclosed as they involve national security,” Tang said.
Kwan was seen leaving a police station on Monday afternoon, without commenting on his case or confirming if he had been formally arrested.
Officials also announced that some of the exterior netting used on scaffolding at the housing estate did not meet fire-resistance standards.
Seven of the 20 samples collected at various locations in four buildings of Wang Fuk Court did not meet fire-resistance test standards, said chief secretary Eric Chan.
The city has seen an outpouring of grief in recent days.
Thousands have laid flowers and paid their respects over a three-day mourning period, with some of the notes left at the site calling for accountability.