Mikhail Gorbachev, who resigned as Soviet president 20 years ago , has urged Prime Minister Vladimir Putin to follow his example and step down.
Gorbachev says if Putin stepped down now he would be remembered for the positive things he did during his 12 years in power.
The former Soviet leader spoke on Ekho Moskvy radio today after a demonstration against Putin drew large crowds.
The 80-year-old Gorbachev carries little weight in Russia today. And while many Russians have grown weary with Putin's rule, his opponents are split among numerous groups. They have no clear leader who could challenge Putin in the March presidential election.
Tens of thousands of demonstrators cheered opposition leaders and jeered the Kremlin in the biggest show of outrage yet against Prime Minister Vladimir Putin's 12-year rule.
The Moscow demonstration was even bigger than a similar rally two weeks ago, signaling that the protest movement ignited by the fraud-tainted 4 December parliamentary election may be growing. Protest were also held in dozens of other cities and towns across Russia.
Rally participants densely packed a broad avenue, which has room for nearly 100,000 people, about 2.5 kilometers (some 1.5 miles) from the Kremlin, as the temperature dipped well below freezing. They chanted "Russia without Putin!"
A stage at the end of the 700-meter (0.43 mile) avenue featured placards reading "Russia will be free" and "This election Is a farce." Heavy police cordons encircled the participants, who stood within metal barriers, and a police helicopter hovered overhead.
Alexei Navalny, a corruption-fighting lawyer and popular blogger, electrified the crowd when he took the stage. A rousing speaker, he had protesters shouting "We are the power!"
Navalny spent 15 days in jail for leading a protest on Dec. 5 that unexpectedly drew more than 5,000 people and set off the chain of demonstrations. Since his release, he has helped to further galvanize the opposition.
Putin's United Russia party lost 25 percent of its seats in the election, but hung onto a majority in parliament through what independent observers said was widespread fraud. United Russia, seen as representing a corrupt bureaucracy, has become known as the party of crooks and thieves, a phrase coined by Navalny.
"We have enough people here to take the Kremlin," he shouted to the crowd. "But we are peaceful people and we won't do that — yet. But if these crooks and thieves keep cheating us, we will take what is ours."
The recent protests in Moscow and other cities have dented Putin's authority as he seeks to reclaim the presidency in a March vote. The Kremlin has responded by promising a set of political reforms that would allow more political competition in future elections.
But protest leaders say they will continue pushing for a rerun of the parliamentary election and punishment for officials accused of vote fraud. They say maintaining momentum is key to forcing Putin's government to accept their demands.
"We don't trust him," opposition leader Boris Nemtsov told the rally, urging protesters to gather again next month to make sure that the proposed changes are put into law. Along with liberals, the rally also drew Communists and nationalists.
Nemtsov called on the demonstrators to go to the polls in March to unseat Putin. "A thief must not sit in the Kremlin," he said.
Former world chess champion Garry Kasparov was among an array of speakers who sought to give the protesters a sense of empowerment.
"There are so many of us here, and they (the government) are few," Kasparov said from the stage. "They are huddled up in fear behind police cordons."
Many in the crowd were young.
"We want to back those who are fighting for our rights," said 16-year-old Darya Andryukhina, who said she had also attended the previous rally.
"People have come here because they want respect," said Tamara Voronina, 54, who said she was proud that her three sons also had joined the protest.
The protests reflect a growing public frustration with Putin, who ruled Russia as president in 2000-2008 and has remained the No. 1 leader after moving into the prime minister's seat due to a constitutional term limit. Brazen fraud in the parliamentary vote unexpectedly energized the middle class, which for years had been politically apathetic.
"No one has done more to bring so many people here than Putin who managed to insult the whole country," said Viktor Shenderovich, a columnist and satirical writer.
Putin has accused the United States of fomenting the protests in order to weaken Russia and has said, sarcastically, that he thought the white ribbons many protesters wear as an emblem were condoms.
In response to Putin's blustery rhetoric, one protester Saturday held a picture montage of Putin with his head wrapped in a condom like a grandmother's headscarf.
"We can't tolerate such a show of disrespect for the people, for the entire nation," journalist and music critic Artyomy Troitsky said in a speech at the rally. He wore a white gown that resembled a condom, mocking Putin's comment.
Although Putin has derided the demonstrators as Western stooges, he has also sought to soothe public anger by promising to relax his grip on the political scene.
He has promised to liberalize registration rules for opposition parties and restore the direct election of governors he abolished in 2004. Putin's stand-in as president, Dmitry Medvedev, spelled out those and other proposed changes in Thursday's state-of-the nation address, promising to restore direct elections to fill half of the seats in parliament and ease rules for the presidential election.
Some opposition leaders welcomed the proposals, but stressed the need for the protests to continue to force the Kremlin to quickly turn the promises into law.
"These measures are insufficient," said Arina Zhukova, 45, another participant in Saturday's rally. "They are intended to calm people down and prevent them from showing up at rallies."
The electoral changes, however, will only apply to a new election cycle years away, and the opposition has stressed the need to focus on preventing fraud in the March presidential election and mounting a consolidated challenge to Putin.
Former Finance Minister Alexei Kudrin, who lost his seat after complaining about increased defense spending, surprised the protesters by saying the current parliament should approve the electoral changes and then step down to allow new elections to be held.
Kudrin, who remains close to Putin, warned that the wave of protests could lead to violence and called for establishing a dialogue between the opposition and the government. "Otherwise we will lose the chance for peaceful transformation," he said.
In another sign of the authorities' efforts to stem the tide of public anger, the presidential human rights commission early Saturday echoed protesters' demands in a statement condemning violations in the vote and calling for the ouster of Central Election Commission chief Vladimir Churov.
It said that allegations of widespread fraud have led to a "moral and political discrediting of the election system and the lower house of parliament, creating a real threat to the Russian state."