Tens of thousands of Russians are expected to take to the streets on Saturday despite Kremlin efforts to ease tensions over disputed elections and Vladimir Putin's expected return to the presidency.

More than 50,000 people have indicated their intention to attend a protest on Moscow's Sakharov Prospect, named after the late leading Soviet dissident Andrei Sakharov. Thousands more have signed up via social networking sites for protests in more than 80 Russian cities.

The protesters are hoping to capitalise on the momentum launched earlier this month, when up to 50,000 people turned out in Moscow alone demanding the Kremlin overturn parliamentary election results that saw Putin's United Russia take a majority in the Duma despite widespread accusations of fraud.

The former Soviet premier Mikhail Gorbachev, the novelist Boris Akunin, the anti-corruption activist Alexey Navalny and Ksenia Sobchak, the Russian "It Girl" and daughter of Putin's mentor, are among those expected to address the crowd. Protesters will don white ribbons to symbolise their opposition to the election results, which they say are a sign of their country's lack of democracy. The oligarch Mikhail Prokhorov, who is running against Putin, also said he would address the rally.

The Russian leadership has played a double game of mocking the protesters while proposing to liberalise the country's political system as it struggles to confront the largest ever challenge to its rule. Putin has twice compared the protesters' ribbons to condoms and repeatedly accused them of being in the pay of the US state department, while Dmitry Medvedev, the more liberal president, has issued a series of proposals to loosen the election laws.

Protest organisers, holding their final organising committee meeting on Friday, said that Medvedev's proposals, issued during his final state of the nation address on Thursday, were not enough.

"It is not an answer – it's not what Bolotnaya expects and not what Sakharov Prospect expects," said the opposition leader Vladimir Ryzhkov, referring to the two protest sites. "Medvedev didn't answer a host of our demands."

Protesters are calling for election results to be overturned, the elections committee chief Vladimir Churov to be fired and political prisoners to be released. They have also begun to turn their attention to a 4 March presidential election, calling on disaffected Russians to vote against Putin as he seeks to return to the Kremlin after four years as prime minister.

In a sign of increasing nervousness, Vladislav Surkov, the Kremlin's secretive chief ideologist, gave a rare interview published on Friday, in which he argued that "the system has already changed".

"People are saying: 'We exist, we have meaning, we are the people,'" Surkov told Izvestiya newspaper. "One cannot arrogantly dismiss their opinions." Surkov is the architect of Russia's "managed democracy" and "power vertical", two terms used to describe the country's soft authoritarian form of governance.

In the same interview, Surkov followed Putin and Medvedev in claiming the protests were organised by outside forces. "Of course there are those who wish to turn the protests into a colour revolution, that's for sure," he said, referring to pro-democracy revolutions that shook Georgia and Ukraine. He appeared to link Russia's protests to the Arab Spring by accusing demonstrators of following the instructions of the US political scientist Gene Sharp, whose book on revolution has been influential in recent popular uprisings. "It's so by the book that it's boring," Surkov said. "I want to suggest to these gentlemen that they cut themselves off from these instructions."

Medvedev on Friday submitted to parliament a packet of draft bills easing rules for registering political parties and presidential candidates. At the same time, he promoted two officials notorious for their hardline background. On Thursday, the deputy prime minister, Sergei Ivanov, a former defence minister and close Putin ally, became the Kremlin chief of staff, a move likely designed to set the stage for Putin's return to the presidency. Medvedev appointed Dmitry Rogozin, an outspoken nationalist who is currently Russia's envoy to Nato, to replace him as deputy prime minister in charge of the military.