Five defendants were in a lift in the Moscow regional court building when they seized the weapons from the two officers escorting them, the Investigative Committee, the state body which handles serious crimes, said in a statement.
When the lift stopped on the third floor of the building and the doors opened, three of the defendants tried to escape but were shot dead by Russian national guard officers. The two others defendants were seriously wounded, the statement said.
Three law enforcement officers were hurt, one of them with a gunshot wound. Two of the three were taken to hospital.
The defendants are accused of being members of a group, dubbed in Russian media the Grand Theft Auto Gang after the computer game. Prosecutors allege the group was responsible for a series of vehicle thefts that in several cases involved killing the cars' owners.
One of the group had fought for Islamic State in Syria before coming to Russia, official TV channel Rossiya 24 said on Tuesday, citing a source in law-enforcement bodies.
(Reporting by Denis Pinchuk and Maria Tsvetkova; Writing by Dmitry Solovyov; Editing by Christian Lowe/Jeremy Gaunt)
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.