Breaking two days of silence, Russian President Dmitry Medvedev has posted on his facebook page that there will be an inquiry into election fraud allegations
Although he said this is not due to protests and disagrees with demands and slogans which have attacked Prime Minister Vladimir Putin.
Tens of thousands rallied in Moscow and other cities on Saturday in the largest anti-government protest in post-Soviet history. They claim the vote was rigged and want to see the back of Putin who has dominated national politics for over a decade.
Security was still out in force on Sunday. Dozens of police interior ministry vehicles and troops encircled some more modest protests.
The hard-line communist Working Russia movement held a demonstration in Moscow’s Revolution Square. They called for redistribution of land and a change to the regime.
Meanwhile holding another rally were hundreds of Russian nationalists.
The group which has little popular support said they would not unite with liberals or left wingers, but echoed Working Russia’s calls for an end to Putin’s rule.