Terrorism has been ruled out.
"We rescued seven people, four of whom unfortunately did not make it", Mr Zheltov said.Police said that the incident happened as the bus driver lost control of the bus.
He said the bus had been towed off the pedestrian underground passage and the rescue operation was now complete.
While health officials said four people had died, interior ministry spokesman Col Yuri Titov said the accident had claimed five lives.
Earlier GAZ offered its experts for working as part of the commission to investigate the causes of the accident.
The Russian Investigative Committee, which investigates major crimes, said the driver told them the brakes did not work.
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The accident occurred on one of the Moscow's busiest roads near the Slavyansky Boulevard metro station.
"According to the driver, the bus was parked and suddenly began to move by itself".
Sirens were blaring around the metro station, as authorities prepared to pull the bus out of the underpass, an AFP correspondent at the scene said.
The police said that "two versions are being examined: the driver failed to manage the vehicle or a malfunction of the vehicle". A helicopter will evacuate the wounded persons.
Monday was an ordinary working day in Russian Federation, where Christmas is celebrated on January 7.
Moscow mayor Sergei Sobyanin took to Twitter to express his condolences to the victims and their families.
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