It was not yet known what caused the accident but passengers quoted by local media said the driver was going fast before the crash.
Rescuers walk beside a crashed bus in Hong Kong, China February 10, 2018.
An inquiry into the accident and the bus company's operation will be set up, Lam said.
Photo The bus crash on Saturday was the deadliest in Hong Kong since 2003.
The dead included 15 males and three females, police said.
The bus was traveling from a horse-racing track in the district of Sha Tin to Tai Po Center in Hong Kong's New Territories when it turned over, shearing off part of its roof, according to news media reports.
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It slid on its side, coming to rest after hitting a lamp post.
The injured passenger told the paper: "It was much faster than I normally felt in a bus".
A full-scale response from the emergency services saw dozens of police, firefighters and paramedics race to the scene to disentangle victims from the battered bus. It was really chaotic on the bus.
KMB bus 872 rolled over during the incident on Tai Po Road on Saturday evening, though the cause of the crash remains unclear. "People fell on top of one another and got tossed around from side to side". Passengers suggested the bus was speeding downhill at the time, and the driver appeared to be upset after he was told off for being late.
He said the franchise bus company would pay $10,000 to each injured person and family of the deceased.
Carrie Lam, Hong Kong's top official, said after the crash a year ago that she didn't believe new laws governing drivers' hours were an answer, and that any solution had to address broader questions of worker shortages.