Russian President Dmitry Medvedev on Sunday ordered an investigation into the allegations of electoral fraud during last week's parliamentary vote.

The announcement came a day after tens of thousands of people rallied in Moscow and other cities to demand the December 4 polls won by Prime Minister Vladimir Putin's ruling United Russia party be annulled and rerun.

In a post on the social media site Facebook, Mr. Medvedev said that “although he does not agree with any slogans or speeches made at the rallies, he has given instructions to check all information from polling station regarding compliance with the election laws.”

Within minutes of his statement, Mr. Medvedev had received over 1,000 comments on his Facebook site, most of them angry and some disrespectful. “Shame!” and “We do not believe you!” were the most common.

Neither the president nor Putin has appeared in public in recent days, as protest organizers sought to harness opposition to the outcome of the polls. Critics accuse Mr. Putin's ruling United Russia party of complicity in widespread vote rigging and other irregularities.

Saturday's rallies in Moscow, St. Petersburg and the Far Eastern cities of Khabarovsk and Vladivostok were the largest to hit Russia since the tumultuous 1990s and were largely peaceful. However, protests in Moscow and St. Petersburg last week triggered a massive police presence and the arrests of hundreds of demonstrators.

French Foreign Minister Alain Juppe on Sunday urged Russia's leaders “to hold a dialogue, to avoid violence, and to let the opposition demonstrate and learn the lessons for the organization of the next presidential elections.”

Juppe also criticized Putin's plan to return to the presidency by swapping places with Mr. Medvedev. He said people do not like it very much when one plays with the democratic process. “To say that I am prime minister and you can have the presidency — and vice-versa — that is something that ends up angering people,” Juppe added.

Last month, Mr. Putin formally accepted his party's nomination to return to the presidency — a post that analysts have said he is certain to win. He announced his intentions in September, confirming a deal under which he would appoint President Medvedev as his prime minister.

The planned job swap has angered many in Russia, who said it would strengthen authoritarian rule and clear the way for Mr. Putin to become Russia's longest-serving leader since communist times.

If he regains the presidency, the 59-year-old Mr. Putin could serve two more 6-year terms and remain in power until 2024. He was first elected president in 2000.