Tens of thousands of people took to the streets of Moscow and other cities across Russia Saturday to protest alleged election fraud in parliamentary elections won by Prime Minister Vladimir Putin's ruling United Russia party.

Police reported at least 20,000 demonstrators on Moscow's Bolotnaya Square across the river from the Kremlin, though organizers put the figure at around 50,000. Moscow authorities had given permission for 30,000 people to gather there.

Helicopters patrolled the skies and security trucks and riot police were deployed in the area. There have been no reports of clashes or widespread arrests.

Rallies kicked off in several other cities throughout the vast country, including in the Pacific port city of Vladivostok, where several hundred gathered, many holding banners reading “The rats should go!”

At least 7,000 people gathered in St. Petersburg, while in the city of Khabarovsk, at least 30 people were arrested after an unsanctioned protest began. Protests were also reported in several cities in Siberia.

The rallies follow a violent crackdown on a series of demonstrations earlier this week, after Mr. Putin's party won parliamentary elections Sunday.

The prime minister's party barely held onto the lower house, but opposition parties and observers contend the winning results were probably inflated. The ruling party's leaders have denied cheating.

The parliamentary win puts Mr. Putin on course to win the March election, which would return him to the president's office. He was president in 2000-2008 and effectively remained the country's leader while prime minister.

Thursday, he lashed out at U.S. Secretary of State Hillary Clinton for questioning the election, accusing her of instigating protesters in order to weaken Russia.