More than 45,000 people have been evacuated from 200 "targets" in dozens of Russian cities after a wave of anonymous bomb threats were made over the past three days, amid speculation of either foreign interference or a domestic anti-terror drill.

Today, 15,000 people were evacuated from places in Moscow, including Red Square, after calls were made to shopping centres, three railway stations and at least four universities.

Anonymous callers are reported to be using the internet to alert emergency services or facilities directly, claiming places had explosive devices hidden inside.

Since Tuesday dozens of schools, universities, shopping centres, railway stations, airports and government offices have been evacuated and inspected by police in 29 cities all over Russia - from Kaliningrad in the west to Vladivostok in the far east.

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No traces of explosive devices have been found in any of the buildings, the Meduza news outlet reported.

Anonymous sources in law enforcement told Interfax news agency that mass evacuations were prompted by a spam attack "masterminded from abroad". State-run RIA Novosti news agency cited another anonymous source that said bomb threats were "coming from Ukraine".

But several regional news outlets quoted unidentified military officials who maintain that the evacuations are part of a Russian anti-terror exercise, performed in preparation for the staging of next year's World Cup finals.

An administrator of a mall in Bryansk, who a call, told the Kommersant newspaper that the number displayed on her phone had 15 figures in it and started with +88, the country code for Bangladesh.

The caller spoke in Russian and told her to "leave the building" because "there is a bomb inside".

The most recent call identified Red Square, the main tourist attraction point in Moscow, next to the Kremlin, as a supposed target.

In all cities investigations have been opened into "knowingly false reports of a possible explosion", a criminal offence in Russia punishable by up to five years in prison.

Dmitry Peskov, the Kremlin spokesman, refused to comment on the situation and redirected all inquiries to Russia's security services.

Russia's law enforcement bodies so far have made no official statement.

The calls are difficult to trace because they are made over the internet and are processed by different servers, including ones abroad, Gennady Gudkov, a Moscow-based security expert and former parliamentarian said.

"That's why the law enforcement hasn't been able to catch anyone so far," he told the Daily Telegraph, adding that the wave of calls is likely to be a criminal organisation testing new technologies rather than an anti-terrorism drill, because people would usually be warned in advance.