Russia's President Dmitry Medvedev signed a bill that widens the powers of the Federal Security Service, the KGB's main successor agency.
The bill would allow the agency, known by its initials FSB, to issue warnings to people suspected of preparing to commit crimes against Russia's security.
Perpetrators face fines or arrest to up to 15 days.
Critics said this power could be used to intimidate government opponents and stifle protests.
The bill raised doubts about Mr Medvedev's commitment to promoting full-fledged democracy and freedom of expression.
Mr Medvedev has taken a less hard line on many issues than his predecessor Vladimir Putin, a former KGB officer and later head of the FSB.
Mr Putin is now prime minister and many see his intolerance of dissent as influencing the Kremlin.