By Steven Eke
BBC Russia analyst
The European Union has called on Russia to respect freedom of expression and freedom of assembly, after a weekend crackdown on demonstrators.
Human rights groups accused police of being heavy-handed
A spokeswoman for the EU said the body was very concerned about the police action in Moscow and St Petersburg.
Earlier, Russia's human rights ombudsman said he intended to investigate the incident.
Police are accused of randomly beating demonstrators, journalists and even passers-by.
The EU spokeswoman said the European Commission would continue to raise the issue of respect for basic freedoms in its regular meetings with Russian officials.
Human rights groups in Russia say they intend to set up a commission to investigate why such force was used against peaceful demonstrators in Moscow on Saturday, and then St Petersburg, Russia's second city, on Sunday.
They have been encouraged by a pledge from Vladimir Lukin, Russia's official human rights ombudsman, who said he believed police had exceeded their authority.
In a key election year, the Russian authorities appear nervous. They have begun to use a degree of violence against demonstrations not seen since the 1980s, when the Soviet Union still existed.
Demonstrators argue that they have a constitutional right to participate in protests unimpeded by the authorities. They say a raft of laws and regulations - some introduced very recently - limiting such protests are simply unconstitutional.
Chess star Garry Kasparov was arrested on Saturday
That is not an analysis the authorities agree with. Russia's top political commentators say there is a logic to the authorities' actions.
Russia will hold parliamentary elections in December and then a presidential vote in March next year.
It is already clear that the authorities' key strategy is to consolidate support for their parties and candidates by stressing unity in the face of an external enemy - namely the West.
In response to complaints from foreign governments that their journalists were also attacked by police, Russian diplomats have accused them of "unobjective coverage" of the protests.