Officers from the criminal investigation department and special forces detained "three members of an armed criminal group" that specialised in robbing couriers ferrying bags of cash, police said in a statement released after the operation yesterday.
Police officers fired their service pistols as they attempted to capture the suspects parked close to the Paveletsky mainline rail station.
Witnesses posted photographs on social media of bullet holes in the windows of a nearby office block.
The suspects managed to flee at high speed in their stolen black Mercedes SUV prompting a car chase with police. One suspect was detained after running into nearby Danilov monastery, the seat of the Orthodox Church's Patriarch, video footage released by police showed.
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During the chase, the suspects crashed into a police car and collided with five other cars, police said.
In their last crime, the alleged robbers had grabbed more than 8 million rubles (USD 146,000) in an attack on a cash courier in May, police said.
"The detained gang members are suspected of more than 20 robberies," the Moscow police spokesman Andrei Galiakberov told TASS state news agency.
Police confiscated two handguns that fire rubber bullets modified to make them more deadly, as well as knives, masks and a wig and a sledgehammer possibly used to break car windscreens.
Russian television said the men came from Moldova, Georgia and Tajikistan. They are being questioned and have not so far been charged.