MOSCOW - Tens of thousands of people on Saturday held the largest antigovernment 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 was no indication the opposition was strong enough to push for real change from the prime minister or his ruling party.

Nonetheless, Putin 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 retained a majority.

The independent Russian election-observer group Golos said Saturday the United Party had "achieved the majority mandate by falsification," international observers reported widespread irregularities, and the outpouring of Russians publicly denouncing Putin throughout the country undermined his 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 president of Russia from 2000 to 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 had been held in support of the election results in recent days.

"We respect the point of view of the protesters, 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."

In the most dramatic of Saturday's protests, a vast crowd jammed 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.

About 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 characteristically takes 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 gatherings to small attendance, most of the protests Saturday were sanctioned.