Thousands of police and interior ministry troops are being deployed in Moscow, after protesters accused the authorities of electoral fraud.
Lorries filled with troops were reported driving into central Moscow.
Interior ministry spokesman Col Vasily Panchenkov said they wanted "to ensure the security of the citizens".
At least 300 protesters were arrested overnight in Moscow, after parliamentary elections said to have been marred by flagrant violations.
Several thousand people had taken to the streets in one of the biggest opposition gatherings in the centre of the capital in years.
Alexei Navalny, a leading campaigner against corruption and fierce critic of Prime Minister Vladimir Putin, was among those detained.
A counter-demonstration by Putin supporters was held beside Red Square on Tuesday.
Observers from the Organisation for Security and Co-operation in Europe (OSCE) reported that Sunday's election had been slanted in favour of Mr Putin's party, United Russia.
United Russia won the election with just under 50% of the vote, a sharp drop in its support.
Correspondents say the result reflects Mr Putin's declining popularity ahead of his bid for the Russian presidency in March.