( CNN ) -- Braving bitter cold , Muscovites in favor of Russian Prime Minister Vladimir Putin and those convinced parliamentary election results were rigged took to the streets Saturday . The dueling rallies were held about six weeks after the last major anti-government demonstrations . Putin is seeking the presidency in the March elections and will represent his United Russia party . The move is the latest step toward Putin 's reclaiming the presidency after switching to the prime minister 's office because of a law barring him from serving more than two consecutive terms as president . Russia 's third-richest man , billionaire New Jersey Nets owner Mikhail Prokhorov , is running against him . Joining tens of thousands of marchers , Prokhorov told CNN Saturday the protesters `` are my potential voters . And I will do my best to help them to live in an open , competitive Russia . '' The state-run Ria Novosti news agency , quoting police figures , said the opposition rally in Moscow gathered 33,000 participants , while the pro-government event was attended by 150,000 . But anti-Putin organizers said their numbers were close to 160,000 . The anti-Putin faction , calling for free and fair elections , carried banners , ribbons and signs . Among them was one depicting a rat with the message `` Put in Trash . '' A pro-Putin rally in Ekaterinburg featured music and a wood-burning stove to help marchers deal with the subzero temperatures . Putin has brushed off widespread criticism that the December 4 parliamentary elections in Russia were falsified . He said their results `` reflect the actual lineup of forces in the country , as well as the fact that the ruling force -- the United Russia party -- has lost certain positions . '' The results caused mass protests in December . At that time , President Dmitry Medvedev announced sweeping political reforms , an effort to address discontent . Speaking before the newly elected parliament members in the Kremlin 's St. George Hall , Medvedev proposed that Russia return to direct elections of regional governors ; simplify the registration of political parties and presidential candidates ; and establish a new editorially independent national public TV channel . Medvedev also called for lifting many of the political restrictions imposed in the past several years by Putin . CNN 's Phil Black contributed to this report .
Pro- and anti-government rallies are held in Moscow . Prime Minister Putin says parliamentary elections in December were fair . Opponents claim the results were rigged . Putin is running for president in March .