Moscow ? Tens of thousands of people held the largest anti-government protests that post-Soviet Russia has ever seen to criticize electoral fraud and demand an end to Vladimir Putin’s rule. Police showed surprising restraint and state-controlled TV gave the nationwide demonstrations unexpected airtime, but there is no indication the opposition is strong enough to push for real change from the Putin or his ruling party.

Nonetheless, the prime minister seems to be in a weaker position than he was a week ago, before Russians voted in parliamentary elections. His United Party lost a substantial share of its seats, although it retains a majority.

The independent Russian election-observer group Golos said Saturday that “it achieved the majority mandate by falsification,” international observers reported widespread irregularities, and the outpouring of Russians publicly denouncing him throughout the country undermines Putin’s carefully nurtured image of a strong and beloved leader.

Putin “has stopped being the national leader — in the eyes of his team, the ruling political class and society,” analyst Alexei Malachenko of the Moscow Carnegie Center wrote on his blog.

Putin, who was the president of Russia in 2000-2008 before stepping aside because of term limits, will seek a new term in the Kremlin in the March presidential elections. The protests have tarnished his campaign, but there is not yet any obvious strong challenger.

A statement released late Saturday by Putin’s press secretary, Dmitry Peskov, acknowledged the day’s protests by people “displeased” with the elections but noted demonstrations in support of the elections in recent days.

“We respect the point of view of the protestors, we are hearing what is being said, and we will continue to listen to them,” the statement said. “The citizens of Russia have a right to express their point of view, in protest and in support, and those rights will continue to be secured as long as all sides do so in a lawful and peaceful manner.”

The most dramatic of Saturday’s protests saw a vast crowd jam an expansive Moscow square and adjacent streets, packed so tight that some demonstrators stood on others’ toes. Although police estimated the crowd at 30,000, aerial photographs suggested far more, and protest organizers made claims ranging from 40,000 to 100,000 or more.

Elsewhere in Russia, some 7,000 protesters assembled in St. Petersburg, and demonstrations ranging from a few hundred people to a thousand took place in more than 60 other cities. Police reported only about 100 arrests nationwide, a notably low number for a force that takes characteristically quick and harsh action against opposition gatherings.

The police restraint was one of several signs that conditions may be easing for the beleaguered opposition, at least in the short term. Although city authorities generally refuse opposition forces permission to rally or limit the gatherings to small attendance, most the protests Saturday were sanctioned. In a surprise move, Moscow gave permission for up to 30,000 people to rally and police took no action when the crowd appeared to far exceed that. Police also allowed an unauthorized protest to take place in Revolution Square.

Yet the concessions may be only a way of buying time in hope the protests will wither away. The opposition says the next large Moscow protest will be on Dec. 24. What it will do in the interim to keep morale high is unclear. In addition, the social media that nourished Saturday’s protests may be coming under pressure. A top official of the Russian Facebook analog Vkontakte said this week his company has been pressured by the Federal Security Service to block opposition supporters from posting. On Friday, he was summoned by the service for questioning.