Voters could no longer cast ballots "against all" and in most regions there was no longer a minimum turnout required to validate the election.
In a few regions, all voting was by party, meaning no ballots could be cast for individual candidates and parties had to clear a higher minimum threshold of 7 per cent to gain seats.
Candidates from 14 parties are competing in the regional polls which critics say do not represent genuine pluralism.
|Critics claim the new election rules were|
designed to stifle dissent [Reuters]
Two of them, pro-Putin party Just Russia and the dominant Kremlin-controlled United Russia, are the favourites.
Exit polls conducted by VTsIOM, the All-Russian Centre for the Study of Public Opinion, showed United Russia retaining its support base in most regions.
But the organisation said Just Russia would gain a foothold and take nearly half the votes in the Stavropol region.
Official preliminary results are expected on Monday.
Boris Gryzlov, the United Russia leader, said late on Sunday that his party was likely to have a majority in nine of the regions, making it "easy for us to reach [an] agreement with parties supporting the president" to form a coalition government, the RIA-Novosti state news agency said.
Barred from ballots
"They know that with free and fair elections and no censorship they will not last long''
Garry Kasparov, Other Russia opposition leader
Garry Kasparov, who leads the Other Russia opposition movement, said: "Russia today technically is a police state and this corrupt and unethical Putin regime is trying to survive at any cost.
"They know that with free and fair elections and no censorship they will not last long,'' the former world chess champion said.
Voters in St Petersburg were dismayed that some parties had been barred from the ballot.
Yabloko, a liberal party, was excluded by a ruling that more than 10 per cent of the signatures it gathered to enter the race were invalid.
Another party, the liberal Union of Right Forces, was barred from the ballot in four regions because in some cases candidates withdrew under pressure from threats or with promises of jobs, its leader said.
Over the weekend, police in St Petersburg dispersed one of the largest opposition rallies in Russia in years, mainly complaining against the sidelining of opposition parties.