President Dmitry Medvedev used his Facebook page Sunday to disclose that he had ordered an investigation into reports of election fraud, a statement his audience greeted with derision.

The posting quickly went viral, and it drew more than 8,000 mostly offended and even offensive comments in a little over six hours, revealing the depth of the disillusionment with Medvedev, Prime Minister Vladimir Putin and their government. Tens of thousands of Russians spoke up in demonstrations across the country Saturday, protesting the Dec. 4 parliamentary elections, and they apparently had no intention of returning to their former silence.

“Shame!” was a frequent comment, along with “You’re pathetic.”

The commenters’ posts Sunday revealed astonishing candor and courage. It’s one thing to stand in a Moscow crowd of up to 40,000, according to estimates, and call for new elections. It’s another matter to advertise your anger and disgust on the president’s Facebook page, where it doesn’t take a KGB agent to make a quick identification.

In posting on Facebook, Medvedev was attempting to respond to Russians who organized Saturday’s protest online, who are angry because they suspect the election was rigged in favor of the ruling United Russia Party.

“I agree neither with the slogans, nor the statements voiced at the protests,” Medvedev wrote. “Nevertheless, I have ordered checks into all the reports from polling stations, regarding the compliance with the election laws.”

One reason for the skepticism that greeted his remarks: Medvedev is the head of United Russia and was the top candidate on its party list in the election. He nominates the chief prosecutor and judges, who might not be eager to pursue those working on behalf of the ruling party.

Medvedev, famous for tweeting and carrying an iPad, routinely orders investigations into all sorts of matters: the beating a year ago of the journalist Oleg Kashin, the death of lawyer Sergei Magnitsky, the forest fires that burned out of control in 2010, a blaze at a retirement home in 2009. Nothing has come of those.

When he blandly announced Sept. 24 that he would relinquish the presidency after one term so that Putin could run in March and take it back, he finally lost his credibility among Russians who had been counting on him as a progressive counterpoint to Putin.

“I haven’t noticed anything good coming from your presidency,” one commenter wrote Sunday. “And on my meager doctor’s salary it has become even worse. Leave now, and don’t wait for the Tahrir Spring. It is going to happen, I promise you.”

Frustration was also evident at Medvedev’s talk of an investigation when protesters were demanding new elections. “Have you lost your mind? How many do you need? 100,000 at the Kremlin?”

On Thursday, Vladimir Churov, head of the Central Election Commission and a longtime Putin ally, said he asked prosecutors to look into the videos posted on the Internet that showed purported violations. He promised that infractions would be pursued but suggested that many may have been faked, filmed in someone’s apartment. “Those who created, commissioned or sponsored them will be held to account,” he said.

That reminded one commenter of Putin’s accusations that same day against Secretary of State Hillary Rodham Clinton, saying that she criticized the election before the vote was counted and signaled the protests to begin. Earlier, Putin attacked Golos, Russia’s only independent monitor, because it receives European and U.S. grants.

The commenter said the United States had probably arranged for the huge demonstrations to be filmed in someone’s apartment.

A sentiment heard from many at Saturday’s protest in Moscow was echoed in a comment on Facebook: “I don’t know anyone among my colleagues, neighbors, acquaintances and friends who voted for United Russia. We all have a sense of the real total.”

One comment in particular reflected the tone of the protest, which was dominated by the middle class and the well educated.

“Obviously, he doesn’t agree with Gauss,” one commenter wrote, referring to pioneering mathematician Carl Friedrich Gauss, who lived 200 years ago. Disenchanted Russians argue that United Russia’s reported election results are so improbable as to violate Gauss’s groundbreaking work on statistics.

At Saturday’s rally, Artyom Zhilin, a 36-year-old psychotherapist, and his wife, Alla, a 27-year-old craft-maker, were holding a large sign that depicted Gauss with goat horns coming out of his head. The message: Putin’s supporters like to insult the opposition by calling them goats, and because Gauss’s work doesn’t square with the vote tallies, he must also be against Putin — and thus a goat.

“We really hate stupidity,” Zhilin said.

Correspondent Will Englund contributed to this report.