The overarching theme for the day was “Nodoel!” or “Enough!” as in enough of Mr. Putin and his government. Signs and many petitions called on him not to seek a fourth term in next year’s presidential election. He is expected to run, although he has yet to officially declare his plans.
“We have Putin, we don’t need food,” read one sarcastic protest sign in the Siberian city of Tomsk, where some press reports said 500 people had taken part in the event.
Before Saturday, Open Russia announced that it had organized protests in about 30 cities. Over all, the number of participants was smaller than the tens of thousands who turned out in about 80 cities for protests called by the main opposition leader, Aleksei A. Navalny, on March 26. Mr. Navalny has called for more demonstrations on June 12.
In Moscow, the capital, hundreds of people holding petitions lined the sidewalk near the Kremlin administration building between Red Square and Staraya Ploshad, or Old Square. For a little more than two hours starting around 2 p.m., petitioners filed into a government office to present their letters, many of them written on the spot.
In the days before the protest, the government had deployed construction equipment and barriers near the office that handles such letters, leaving organizers to believe the entrance would be blocked.
After word went out that the letters were indeed being accepted, many more people arrived to stand in line. Organizers said that an early count found that at least 1,500 people had presented petitions in Moscow.
“We must participate in such events to show the authority that more and more people whose rights are being violated are against this,” a 30-year-old marketing specialist who identified herself only as Veronika said as she wrote her letter. Many participants were reluctant to give their names because of the legal problems faced by numerous people who took part in previous protests. “I want to live in a country where laws are observed,” she said.
Another protester who declined to give his full name, Aleksandr, 26, said he had tried to start an emergency services company to work in gas fields and had been blocked at every turn. “They keep telling me that they don’t have the budget, maybe because the prime minister stole $70 billion dollars,” he said, referring to recent accusations against Prime Minister Dmitri A. Medvedev in a YouTube video produced by Mr. Navalny.
“The government does not care about ordinary people — about our salaries, medication, our rights, nothing,” Aleksandr said.
Many of those presenting petitions acknowledged that the relatively low turnout and the government’s general indifference meant the protests would probably not have much of an effect. But they said it was time to start pushing back against an erosion of civil liberties and the country’s poor economic performance.
Open Russia’s Facebook page had a few suggestions about subjects to be addressed in the petitions, including “We are tired of living on poverty-level salaries and pensions”; “We are tired of listening to lies on television”; and “We are tired of driving on bad roads.”
Under Russian law, the government is supposed to respond to such letters in 30 days. Two women who were accepting petitions assigned each one a number and gave the writer a slip of paper with a telephone number to call. Few expected answers, especially to the many letters calling on Mr. Putin to quit.
“They will probably answer that the writer was not suggesting any exact problem so thank you very much,” said Aleksandr Y. Soloviev, 29, the chairman of Open Russia.
The group’s founder, Mr. Khodorkovsky, a former chairman of the oil giant Yukos, spent several years in prison before being pardoned by Mr. Putin in 2013. Since then, he has lived abroad, becoming one of the Kremlin’s most outspoken critics.
The anticorruption theme burst into new prominence on March 26, with marches that included many young people in about 80 Russian cities. The protests were called by Mr. Navalny, who was subsequently jailed for 15 days for organizing them. More than 1,000 people were arrested in Moscow alone and have steadily been brought to court.
Mr. Navalny appears to have hit a public nerve with a series of videos accusing senior government officials of widespread corruption.
His latest video focused on what he said was a group of four bogus charities that spend more than $66 billion annually to maintain a series of luxurious residences for the prime minister.
Mr. Navalny was doused with green dye for a second time on Thursday, and one eye required medical treatment. He appeared on his YouTube channel afterward, tinted slightly green, to answer questions from around the country.
He expressed support for the idea of submitting petitions on Saturday, but he said he doubted that doing so would produce any positive results.
Asked about the Saturday protest last week, Dmitri S. Peskov, Mr. Putin’s spokesman, noted that it was illegal and would be dealt with accordingly. The police in Moscow repeatedly ordered anyone lingering on the sidewalk to move on, but otherwise treated the protesters respectfully.
A day earlier, the government had declared Open Russia, which has its headquarters in Britain, an “undesirable” organization, making it illegal for the parent organization to operate in Russia. The main reason cited for the designation was that the group had organized protests.
In March, Mr. Putin condemned street protests, saying that they would lead to chaos if allowed to continue, noting the violent aftermath of such outpourings in the Arab world and Ukraine in recent years.
On Friday, Ren TV, a Russian television channel that serves as a cheerleader for the Kremlin, broadcast a documentary that portrayed Open Russia as a collection of criminals and drug addicts who cultivate ties with the United States.
No reports about Saturday’s protests appeared on Rossiya 24, the main cable news channel. Reports included one about the opening of Fountain Season in the capital, with the water being turned on after the long winter freeze, as well as the bike-sharing system.
There also seemed to be a less-than-subtle message directed at the protesters, whom the government often accuses of being financed from abroad. The cable station showed a documentary about treacherous military officers who served the enemy during World War II.