The elections took place in the Republics of Karelia, Tuva, and Chuvashia, and in the Astrakhan, Novgodorod, Lipetsk and Sverdlovsk Regions, the Jewish Autonomous Area and the Primorye Territory.
The ruling United Russia party claimed earlier this year that it would secure more than 45% of the party-list votes in Sunday's regional elections.
New election rules, adopted on an initiative by President Vladimir Putin, eliminate single-mandate districts, and the preliminary results of Sunday's voting indicate how strong United Russia's hold is on the constitutional majority in the lower house of the Russian parliament, the State Duma.
Elections to local parliament in the Astrakhan Region, in the south of European Russia, saw United Russia far ahead of the other parties, with 37.61% of votes, the local election commission said.
The nationalist Rodina (Motherland) party emerged second with 16.73% of the vote followed by the Communist Party with 13.72%, the source said, adding that the turnout was 40.8%, with 20% being the lowest margin.
With 98% of the votes counted, United Russia is leading in Chuvashia on the Volga River with 51.48%. The Communists also crossed the 7% barrier with 19.59% of votes and the ultra-nationalist LDPR party with 9.04%. The turnout was 43.66%.
Although only 5% of the votes have been counted, preliminary results in the Tuva Republic in Central Siberia suggest victory for United Russia, with 40.8%.
The left-leaning Party of Life won 32%, Rodina 7.8%, the Communists 6.2%, the Patriots of Russia 3.35% and the LDPR 3.2%.
Turnout topped 50%, the local election authorities said.
In the Sverdlovsk Region in the Urals, United Russia ended up with 15 out of 28 seats in the local legislature, the press service of the local parliament said.
"On Sunday, we re-elected half of the regional Duma - 14 members," the press service said. "The remaining 14 will continue to work for another two years."
Four seats will be held by the Party of Pensioners, and three by the Communists. The Party of Life won two seats, the source added.
Preliminary results suggest that United Russia gathered 38% in Karelia, a republic in northwest Russia, the local election authorities said.
The ruling party is followed by the Party of Life with over 16%, the Communists with 13%, the Party of Pensioners with 12%, and the LDPR with 9%.
Turnout was low at 29%, the election commission said.
United Russia came up with a preliminary result of 52%, local election authorities in Lipetsk, in the south of European Russia, said.
The Party of Life, led by Speaker of Russia's upper house of parliament Sergei Mironov won 12.5%, the Party of Pensioners 10.5% and the Communists 10%.
The election authorities said the turnout was 35.5%.
The local election commission said United Russia took the lead with 43.75% of the votes in the Novgorod Region in the northwest of European Russia.
The other parties that overcame the 7% barrier were the Communists with 14.68%, Free Russia with 11.03% and the LDPR with 7.03%.
United Russia secured 48.34% of the votes, followed by the Communists with 12.39% and the Party of Pensioners with 9.31%, said the local election officials in Primorye in Russia's Far East.
Preliminary results indicate that United Russia won 55.32% of the votes, the election authorities in the autonomy in Siberia said. The Communists gathered 18.54% and the Party of Pensioners 9.92%.
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The growing outright rivalry between the United States and China gives Russia more foreign policy weight, enabling it to assume the role of a balancer. So far it has been doing so rather skillfully. Today it may participate in a joint naval exercise with China that Beijing positions as outwardly anti-American. But tomorrow it can team up with the naval forces of the Old World.