Protesters say the bill will end political life in the streets
Public protests near government buildings, on roads or near pipelines could soon be banned in Russia.
The lower house of the Russian parliament (Duma) has passed the first hearing of a bill which its critics say will restrict freedom of debate.
Members of a political opposition group were arrested after protesting against the ban outside the Duma.
President Vladimir Putin pledged to defend Russian democracy when he was re-elected earlier this month.
Human rights campaigners have condemned the new legislation as unconstitutional and undemocratic.
Security
Under the draft, which was passed with 294 votes to 137 and needs to pass two more readings, rallies and protests will not be allowed near official buildings, embassies and offices of international organisations.
It also outlaws protests near major roads and environmentally hazardous industrial sites, schools, kindergartens, hospitals, stadiums, concert halls and religious centres.
The government justifies the bill, saying that public events near such sites could threaten their security.
As parliament met to debate it, police dispersed a small group of protesters outside; several were detained.
Among those arrested was the deputy head of the liberal opposition group Yabloko, Sergei Mitrokhin.
He told the protesters: "We will continue to stage these demonstrations even if they pass this draconian law."
A senior member of Communist faction in the Duma, Sergei Reshulsky, said: "This would be the end of political life in the streets."
The BBC's Steve Rosenberg, in Moscow, said that with the support of the pro-Kremlin "United Russia" party, which dominates the Duma, the draft law looks set to sail through parliament.