MOSCOW (AFP) - Russian President Dmitry Medvedev on Sunday ordered election officials to check reports of vote fixing following a national protest over an election that handed a disputed victory to the ruling party. Medvedev said he flatly disagreed with the idea of staging fresh elections but had already issued instructions for a closer look at the reports of rampant ballot stuffing and cases of officials fixing the vote count. "I disagree with the slogans and declarations made at the meetings," the tech-savvy Medvedev wrote in his Facebook account. "Nevertheless, I have issued instructions to check all polling station reports about (failure) to follow election laws," Medvedev wrote. Saturday's historic demonstrations near the Kremlin saw more than 50,000 people deride the outcome of December 4 elections that were widely seen as a litmus test for Vladimir Putin's planned return to the presidency next year. The protests were the largest to hit the Russian capital since the tumultuous 1990s and levelled some of the most intense political pressure at Putin since he first rose to the presidency in 2000. The former KGB agent currently serves as prime minister after making Medvedev his hand-picked presidential successor in 2008 and intends to return to the Kremlin for up to 12 more years in March elections that he appears destined to win. But scenes similar to those witnessed Saturday in Moscow were also replayed on a smaller scale across the industrial hubs of Siberia and the Urals - a sign that Putin's path back may be more fraught than it first appeared. Putin stayed out of the limelight over the weekend while his spokesman issued a carefully-worded statement that sounded a cautiously conciliatory note. "We respect the point of view of the protesters. We are hearing what is being said and we will continue to listen to them," Putin spokesman Dmitry Peskov said in the overnight statement. Medvedev's own comments suggest the two leaders - seen as close allies despite the president's more liberal reputation - are keen to quickly stamp out the most serious political flare-up of Putin's 12-year rule. But Medvedev fell far short of satisfying the opposition's main demand to stage new elections. Former cabinet minister turned Kremlin critic Boris Nemtsov called Medvedev's Facebook message "a mockery". "These are worthless instructions ... that are not going to calm anyone down," Nemtsov told Moscow Echo radio. Rally organisers have already threatened to return to the same Moscow square en masse on December 24 and possibly to hold smaller rallies at various locations before then. Yet analysts point to a series of small but significant changes in state policy in the past few days that hint at serious official concern about the public discontent. One of Saturday's biggest surprises came in the evening when state TV - scorned by the Internet community for its ban on coverage of post-election unrest - took the unusual step of leading its news broadcasts with rallies. A Kremlin source told the popular gazeta.ru news site that the decision to run the mainly-balanced reports was taken by Medvedev himself. The Kremlin source added that Medvedev had also instructed the Moscow police to handle the protesters "extremely gently" after seeing more than 1,000 activists bundled away by riot police the previous week. But dozens of people were still arrested in the regions as officials scrambled to respond to the re-emergence of political activity in cities that had stayed quiet since the early post-Soviet times. "This is an entirely new situation. This is a lot of people for the provinces," said Alexey Malashenko of the Carnegie Moscow Centre. The biggest regional rallies saw some 5,000 people come out in Novosibirsk - Russia's third largest city and the heart of Siberia - and the industrial hub of Chelyabinsk that Stalin developed in the Ural Mountains in the 1930s. "This is the start of a new stage," said Yevgeny Gontmakher of the Institute of Contemporary Development centre set up by Medvedev in 2008. "People have developed a taste for mass demonstrations and are now ready to rise up in response to anything," Gontmakher said. Analysts said rapid social change and the Internet's growing penetration in Russia may have caught Kremlin strategists off guard after a decade in which they could mould public opinion through state-controlled media. "The elections are approaching and people's trust is low," said Carnegie analyst Malashenko. "This means that the ruling class has to think about how it should behave next."