Among the locations affected are three of the capital's biggest railway stations, more than a dozen shopping centers - including GUM, located next to Red Square - and at least three universities, the leading First Moscow State Medical University, and the Moscow State Institute of International Relations among them. Social media accounts show bemused crowds milling passively outside evacuated buildings, and there have been no reports of disturbances of public order.
Numerous bomb threat calls came from Ukraine, according the news agency RIA. Emergency services are working.
By Tuesday, the anonymous threats were reported in Perm, Novosibirsk, Yekaterinburg and other cities, forcing the evacuation of an estimated 45,000 people.
"Apparently, this is nothing else but phone terrorism, but all these messages should be checked", the source said.
"The only goal is to set off destructive processes, to sow panic".
Three shopping malls in Moscow have been cleared by authorities, the Tass news agency reported.
The anonymous calls came from Internet dialing systems and could not easily be traced, official news agencies reported.
"People were evacuated at 30 sites, in total more than 20,000 people were taken outside, this number is still being specified", an emergency services official told Russian news agency TASS.
The Interior Ministry and Security Council declined to comment.
Frants Klintsevich, deputy head of the Defense Committee in the upper house of parliament, said: "There's never been anything like this before, it's 100 percent organized telephone terrorism".