Three of Moscow’s main train stations were being checked on Wednesday, along with the city’s famous GUM department store near Red Square, and more than 20 other buildings, the news agency said.
GUM said on its website it was temporarily closed “for technical reasons.” A Reuters TV cameraman said he saw police with sniffer dogs checking the building.
Russia has this week experienced a wave of hoax bomb threats.
Citing an unnamed source in the emergency services, RIA said the hoaxes had so far affected more than 20 Russian towns and cities.
All of the calls had so far turned out to be false alarms. When asked about the matter, a Kremlin spokesman referred reporters to the police.
RIA cited its source as saying that many of the hoax calls may have been made from Ukraine.
Relations between Moscow and Kiev are at a low after Russia annexed Ukraine’s Crimea in 2014 and pro-Russian separatists in eastern Ukraine rebelled against Kiev’s rule.