MOSCOW (AP) ― 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 prime minister 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 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. Just as striking, police allowed a separate unauthorized protest to take place in Revolution Square.

State-controlled television, which generally ignores or disparages opposition groups, broadcast footage not only of the Moscow protest ― which was so big it would have been hard not to report ― but in several other cities as well.

United Russia official Andrei Isayev on Saturday acknowledged that the opposition “point of view is extremely important and will be heard in the mass media, society and the state.”

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.

Meanwhile, though United Russia may be shaken by the last week’s events, it still can count on a large cadre of supporters. The head of its youth wing, Timur Prokopenko, was quoted by the Interfax news agency as saying he had nearly 170,000 activists “who are ready at moment to go to rallies” in support of the government.

Saturday’s Moscow protest was notable not only for its size, but also for attracting political forces from across the spectrum ― from liberals to communists to extreme nationalists.

“United Russia made a miracle, prompting all of us to unite against it,” nationalist leader Konstantin Krylov told the rally.

Thousands of protesters also were allowed to march from a gathering place near the Kremlin across downtown to a square where the main rally was held. Police were out in force, blocking all side lanes to prevent the demonstrators from approaching government buildings.

“Russia will be free!” “Russia without Putin!” “United Russia is a Party of Crooks and Thieves!” protesters chanted.

“We will fight to the end, to the cancellation of this shameful, false election,” said Grigory Yavlinsky, leader of the liberal Yabloko party that failed to make it to parliament in last Sunday’s vote. “We are launching a campaign to drive Putin from power.”

The organizers sought to send a message of unity, urging the crowd to respect the diversity of speakers’ views. At one point, the audience booed a military veteran when he called for the restoration of the Soviet Union, but chanted slogans of support when he denounced the vote-rigging and said the army was with people.

“The army is with us, 80 percent of officers hate the defense minister,” retired Maj.-Gen. Yevgeny Kopyshev shouted.

The organizers also praised police for helping maintain order, as demonstrators chanted “Police with people!”

The rally demanded the cancellation of the election results, the punishment for officials responsible for vote-rigging, registration of the opposition parties that were denied it, liberalization of the electoral law and holding new elections. The organizers urged protesters to brace for another rally in two weeks.

“We’ll come again!” the crowd chanted.

The Moscow organizers appeared to realize they are facing a tough challenge of keeping protest momentum.

“Nothing will change it if it remains a single rally,” said Sergei Parkhomenko, the editor of Vokrug Sveta monthly magazine who was one of the demonstration’s organizers. “It must be the first in a long series of protests.”

Vladimir Milov, a former energy minister who is now an opposition activist, also acknowledged that the organizers need to plan their strategy to preserve the protests’ energy. “Otherwise people will just grow tired and stop attending the rallies,” he said, adding that the opposition must focus on next year’s presidential election.