In Moscow, security is being stepped up ahead of a protest rally on Saturday.
Demonstrators have been granted permission to take to the streets although police, who doused marchers earlier this week, have vowed to stamp out any illegal activity.
The allegations of electoral fraud which have sparked protests have been denied by the Central Electoral Commission. It has confirmed the official result of Sunday’s poll.
Vladmir Putin’s United Russia will have 238 seats in the Duma. The party retains its majority although it has lost 77 seats.
Opposition parties have demanded new elections while President Dmitry Medvedev has said claims of electoral irregularities need to be looked into.
The protests will be peaceful say the demonstrators.
“Rallies which are taking place in Russia are the most civilised protests among those which happen worldwide,” said opposition activist Yevgenia Chirikova. “There is no broken glass, no overturned or burned cars. This is a civilised citizens’ protest against a party of swindlers and thieves, against them depriving us of free and fair elections.”
By midday on Friday, nearly 60,000 people using Facebook and the Russia site VKontakte had pledged to turn up and take to the streets on Saturday. Rallies are also expected in dozens of other cities.