With 98% of the vote counted, United Russia whose candidate list was headed by President Vladimir Putin, are in the lead followed by the Communists with 11.6%, the ultranationalist Liberal Democratic Party with 8.2%, and the loyalist A Just Russia with 7.8%.
Only four parties have overcome the 7% barrier required to take seats in the fifth 450-seat State Duma. Election turnout has been estimated at 63%.
Chechnya, a troubled Russian republic in the North Caucasus, saw the most impressive preliminary results, with United Russia winning over 99%, the local election commission said. Chechnya is run by President Ramzan Kadyrov who has brought relative calm to the republic, although human rights groups accuse him and his supporters of torture and intimidation.
Vladimir Churov, head of Russia's election commission, said the official results of the Duma elections would be announced on December 7-8.
Top international observers, however, said the elections had failed to meet European standards. A joint statement by the Organization for Security and Co-operation in Europe (OSCE) and the Council of Europe said Sunday's poll "was not fair and failed to meet many OSCE and Council of Europe commitments and standards for democratic elections."
The run-up to the elections was marred by a dispute with the OSCE, after its main election monitoring arm refused to dispatch observers for the polls, citing restrictions and visa delays. Moscow in turn criticized "chaos" in the organization and renewed calls for its reform.
Goran Lennmarker, president of the OSCE's Parliamentary Assembly, said Russia's new election law, which raised the threshold for entry to the State Duma from 5 to 7%, and also canceled "the against all" option and minimum voter turnout requirements, had created unequal conditions for smaller political parties, and therefore the elections could not be described as fair.
He also said opposition parties had been pressurized. Shortly before the polls, two anti-Putin meetings in Moscow and St. Petersburg were dispelled by riot police and several opposition figures arrested. One of these, Garry Kasparov, was subsequently jailed for five days.
Referring to President Putin's decision in October to head the United Russia candidate list, Lennmarker said the Kremlin's virtual merger with the party was unacceptable and clearly violated international norms.
Luc van den Brande, the chief Council of Europe delegate, added that the Duma polls were more of a referendum for President Vladimir Putin than a parliamentary election.
Western analysts have also said United Russia enjoyed almost unlimited access to funds, its election campaign dwarfing attempts by other parties to gain a platform.
Central Moscow was dominated by United Russia adverts in the days leading up to the election, with little or no sign of the existence of other parties.
Igor Borisov of Russia's Central Election Commission said the OSCE and Council of Europe allegations were ungrounded and that the commission had not received any official reports from these organizations.
"I believe these conclusions were based on statements from those political leaders who were not satisfied with their parties' election results," Borisov said.
Kimmo Kiljunen, vice president of the Parliamentary Assembly of the Organization for Security and Cooperation in Europe (OSCE), said earlier on Monday that the voting had been fair and democratic, but added that that was merely his personal opinion.
Kiljunen did say, however, that he was extremely surprised at reports that some 99% of the electorate had voted for United Russia in Chechnya. This, he added, was in his experience "impossible".
Observers from the Commonwealth of Independent States, a Russia-led alliance of former Soviet republics, stated on Monday in a report that the Duma elections had been democratic, free and transparent, and urged other international monitors to join their statement on the transparency and democracy of the elections.
President Putin said the parliamentary elections were a demonstration of confidence in his rule.
"I want to thank Russian citizens, all voters, for a high turnout," the president said. "Special thanks to those who voted for United Russia, whose election list I headed, this is an indication of trust."
Putin said the polls showed that Russians would "never allow their country to follow the destructive path taken by some post-Soviet countries." His words were an apparent reference to street protests in Georgia and Ukraine, which brought pro-Western leaders to power in 2003 and 2004.