GWEN IFILL: In Russia tonight, more political turmoil and challenges to Vladimir Putin's power.
Margaret Warner has that story.
MARGARET WARNER: It was a scene without precedent since Putin came to power in Russia 12 years ago, tens of thousands of people demonstrating Saturday in Moscow and other cities.
WOMAN: People want fair elections. People feel that their vote was stolen.
MARGARET WARNER: The crowds accused Putin's United Russia party of fraud in the parliamentary elections held Dec. 4, and demanded they be recounted or rerun.
They expressed growing anger over corruption and one-party dominance of the Russian government. The protesters' unhappiness was galvanized last September when Prime Minister Putin announced he would run for a third term as president next year, switching jobs yet again with the current president, Dmitry Medvedev.
In response, Finance Minister Alexei Kudrin resigned and criticism swelled on Russian Internet sites. Then, last month, Putin was booed by spectators at a martial arts event in Moscow, a rare display of public disapproval captured on this amateur video.
On election day, United Russia eked out a bare majority, losing 20 percent of its seats in the old parliament. And the accusations of fraud came quickly. This video posted on YouTube purported to show ballots that had been filled out ahead of the actual voting.
Anger boiled into the streets last week, with several protests that brought a heavy show of force by police and large numbers of arrests. Among those detained were opposition leader Boris Nemtsov and activist blogger Alexei Navalny.
After international criticism, the government allowed last Saturday's protest to proceed without incident. On Sunday, President Medvedev went on Facebook to promise an investigation. But he didn't endorse the protesters' complaints.
Monday, in Washington, Secretary of State Hillary Clinton welcomed the announcement and said Medvedev has to act.
SECRETARY OF STATE HILLARY RODHAM CLINTON: The proof is in the pudding. We will wait and see how they conduct such an investigation, what the consequences are. So, we're -- we're supportive of the announcement of investigations, and now we hope that it will be followed through on.
MARGARET WARNER: Today, though, Medvedev met with leaders of the four parties that won seats and said the new parliament will meet Dec. 21, despite the claims of fraud.
DMITRY MEDVEDEV, Russian president: In the cases where the rights have been really violated, a fair decision should be made. But the State Duma must begin work. Parliament members always have a lot to do.
MARGARET WARNER: In the meantime, Putin now faces the prospect of new competition in the upcoming presidential election in early March.
Billionaire tycoon Mikhail Prokhorov, who owns the NBA's New Jersey Nets, entered the race yesterday. And the anti-Putin protesters say they are not done. Organizers are calling for another round of mass demonstrations on Christmas Eve.