Correction: An earlier version of this article misstated the number of polling stations operating throughout the country on Dec. 4. The actual number was 95,000.
A joint preliminary report by the Interior Ministry and the Investigative Committee said 2,091 administrative cases have been opened into violations, with the city of Moscow a leader with 492 cases, trailed by the regions of Stavropol (96) and Samara (88), the Kremlin said on its web site.
More than half of the violations had to do with illegal campaign materials, while a quarter involved breaches of rules for public events.
Only 53 criminal cases have been opened nationwide since the Duma campaign kicked off in November, but five of them were dropped, the report said. Suspects have been established for only 10 of the remaining cases.
The elections were won by the pro-Kremlin United Russia with 49.3 percent of the vote, but its opponents and an unprecedented number of grassroots activists accused it of achieving the result through vote-rigging.
The report on the Kremlin web site did not specify which parties stood to benefit from the violations, but added that investigations were ongoing into another 259 complaints about various election-related violations, most of them filed by A Just Russia and the Communist Party.
The tally includes ongoing checks into nine reports of vote fraud, four instances of alleged vote-buying and five cases of ballot-stuffing in various regions. It was unclear whether the checks concerned whole regions or single polling stations, some 95,000 of which operated throughout the country on Dec. 4.
Party and independent vote monitors said between 10 percent and 25 percent of the vote might have been illegally handed over to United Russia. The Central Elections Commission has admitted some violations, but said they amounted to 0.5 percent of the vote and did not affect the distribution of seats in the parliament.
On Dec. 10, some 30,000 to 60,000 protested the elections at a rally on Moscow's Bolotnaya Ploshchad. A follow-up rally is planned at Prospekt Akademika Sakharova on Saturday.