Footage shows people scattering as the bus ran down wide steps before being brought to a halt by the tunnel’s roof.
The incident occurred near Slaviansky Boulevard station in western Moscow.
There is no suggestion it was a terror attack. Russian investigators said the driver told police the vehicle had started to move suddenly.
He tried to apply the brakes but they did not work, the investigative committee said. The crash happened in icy conditions.
The number of people killed was unclear. Health officials said four people had died while interior ministry spokesman Col Yuri Titov said the accident had claimed five lives,
Interfax news agency reported that the bus was not even a year old. Moscow mayor Sergei Sobyanin told reporters at the scene that an inspection of the entire Moscow bus fleet has been ordered.
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