Police in Moscow have agreed to allow demonstrators to take to the streets to protest at the outcome of parliamentary elections which were won by Prime Minister Vladimir Putin's United Russia Party.
The BBC reports that the opposition expects around 30,000 people to gather in a square south of the Kremlin for the protest, which would make it the biggest demonstration in Russia since the collapse of the Soviet Union.
Smaller protests are due to take place in cities across the country.
The protest has been organised via social networking sites like Facebook and Twitter.
Meanwhile, the Council of Human Rights - set up to advise President Medvedev - says the parliamentary elections should be re-run if allegations of widespread vote-rigging are confirmed.
In a statement, the council says reports of election fraud are of deep concern and those who carried out violations should be prosecuted.
Despite the allegations about fraud, the Central Election Commission has confirmed the voting figures for last Sunday's elections, with the United Russia party winning 49% of the vote and the Communist Party a distant second with 19%.