Russian police arrest a political opposition activist at a rally in Moscow.
Photograph: Alexey Sazonov/AFP/Getty Images

Russian citizens can be issued official warnings about crimes that they have not yet committed under powers granted to the security services today.

President Dmitry Medvedev signed off on a new law giving the FSB, the successor agency to the KGB, the right to caution people suspected of preparing acts of extremism, or to jail them for obstructing the agency's work.

The powers appear similar to those enjoyed by Precrime, the police unit in the 2002 Hollywood film Minority Report. "This is a draconian law reminiscent of our repressive past," said Boris Nemtsov, a leader of the Solidarity opposition movement.

Rights activists had hoped Medvedev would rein in the security services, after his predecessor, Vladimir Putin, a former KGB colonel, stuffed his administration with hawkish veterans. The Kremlin's tough stance comes against the backdrop of a disparate but emergent civil movement protesting against corruption and authoritarian government.

Under the new provisions, the FSB will be able to echo Soviet practices. The punishment for ignoring a warning was unclear, but 15-day jail sentences are envisaged for "obstructing an FSB officer's duties". Sergei Ivanenko, a leader of the Yabloko party, called it "the law of a police state". He said: "If such a law exists in a democratic country then it is limited by a very powerful system of civil, public and parliamentary control. In our conditions it will mean absolute power for the security services."

Rights activists, who fear the measures could be used to stifle civil disobedience, had expressed optimism that Medvedev might step in to quash the legislation.

There have been signs of democratisation under Medvedev, while Putin, whom he replaced two years ago, has continued to promote a hardline image from his post as prime minister. But during a meeting with Germany's chancellor, Angela Merkel, a fortnight ago, Medvedev said: "Each country has the right to perfect its own legislation, including that which affects its special services." He added: "What's going on now – I would like you to know this – was done according to my own direct instructions."

Russia's police and security services have looked increasingly clumsy as they try to deal with inventive grassroots activists or single-issue protest groups. One group wears blue buckets on their heads in mimicry of the flashing blue lights on the cars of bureaucrats who terrorise the roads: police arrested several activists but had to let them go because they had committed no crime. Another organisation has been attacked while trying to stop destruction of a protected forest near Moscow.

"Medvedev may smile more than Putin but the face of power hasn't changed," said Eduard Limonov, an opposition politician who plans to run for president in 2012. "The Kremlin is still terrified there will be an Orange Revolution in Russia if people are allowed to gather on the streets."

This Saturday will be the first anniversary of protests started by Limonov and a coalition of activists known as Strategy 31. They meet in Triumfalnaya Square in Moscow at 6pm every 31st of the month to demonstrate in favour of Article 31 of the constitution: the right to free assembly.

Despite each rally being broken up by riot police, the protests have grown steadily, attracting more than 500 people in May. About 180 of them were arrested.

"Instead of thinking of new ways to suppress us, the authorities should listen to our concerns," said Limonov.

Yet democracy activists are often demonised as traitors or extremists in the state-dominated media. This week at its summer camp the Kremlin-backed Nashi youth movement put up a photograph of 83-year-old Lyudmila Alekseyeva, one of the organisers of Strategy 31, on a dummy wearing Nazi insignia.

On Saturday she will go to Triumfalnaya. The protest movement, she said, "will only grow in the face of repression."

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Sound familiar? Communists don't have much imagination.