SÃO PAULO, Brazil -- Political leaders here in Brazil's largest city braced for yet another round of demonstrations on Tuesday night by an increasingly powerful movement that has grown from complaints about bus fares to a broad challenge to political corruption, lavish stadium projects, the cost of living and substandard public services.
The mayor of São Paulo, Fernando Haddad, met on Tuesday morning with representatives of the protest movement, but warned that it would not be possible to revoke the increase in bus fares, citing budget restraints. In the nation's capital, Brasília, officials seemed to be grasping for ways to engage the movement, whose protests rank among the largest and most resonant since the nation's military dictatorship ended in 1985.
"These voices, which go beyond traditional mechanisms, political parties and the media itself, need to be heard," President Dilma Rousseff said in a speech on Tuesday morning. Ms. Rousseff, who has been the target of pointed criticism by some protesters, said that Brazil "awoke stronger" after the protests on Monday night: "The greatness of yesterday's demonstrations were proof of the energy of our democracy."
Gilberto Carvalho, a top aide to Ms. Rousseff, said that the authorities were hoping to establish a dialogue to respond to a widening movement that seems to have caught them by surprise. "It would be a presumption to think that we understand what is happening," he said before senators on Tuesday morning. "We need to be aware of the complexity of what is occurring."
Protesters showed up by the thousands in Brazil's largest cities on Monday night in a remarkable display of strength for an agitation that had begun with small protests over bus fares.
Demonstrators numbering into the tens of thousands gathered here in São Paulo, and other large protests unfolded in cities like Rio de Janeiro, Salvador, Curitiba, Belém and Brasília, the capital, where marchers made their way to the roof of Congress.
Sharing a parallel with the antigovernment protests in Turkey, the demonstrations in Brazil intensified after a harsh police crackdown last week stunned many citizens. In images shared widely on social media, the police here were seen beating unarmed protesters with batons and dispersing crowds by firing rubber bullets and tear gas into their midst.
"The violence has come from the government," said Mariana Toledo, 27, a graduate student at the University of São Paulo who was among the protesters on Monday. "Such violent acts by the police instill fear, and at the same time the need to keep protesting."
While the demonstration in São Paulo was not marred by the widespread repression that marked a protest here last week, riot police officers in Belo Horizonte dispersed protesters with pepper spray and tear gas. In Porto Alegre, in southern Brazil, police officers also used tear gas against protesters.
In Rio de Janeiro, where an independent estimate put the number of protesters around 100,000, televised images showed masked demonstrators trying to storm public buildings including the state legislature, a part of which was set on fire. In Brasilía, the police seemed to be caught off-guard by protesters who danced and chanted on the roof of Congress, a modernist building designed by the architect Oscar Niemeyer.
Such broad protests are relatively uncommon in Brazil, with some Brazilian political analysts describing what appeared to be a political culture more accepting of longstanding high levels of inequality and substandard public services than citizens in some neighboring countries in South America.
"The dangerous news announced on the streets, the novelty that the state tried to crush under the hooves of the horses of São Paulo's police, is that at last we are alive," the writer Eliane Brum said in an essay about the protests.
Brazil now seems to be pivoting toward a new phase of interaction between demonstrators and political leaders with its wave of protests, which crystallized this year in Porto Alegre. There, a group called the Free Fare Movement, which advocates lower public transportation fares, organized demonstrations against an increase in bus fares.
Similar protests emerged in May in Natal, a city in northeast Brazil, and this month in São Paulo, after the authorities raised bus fares by the equivalent of about 9 cents to 3.20 reais, about $1.47, prompting a wave of demonstrations that have grown in intensity.
While the increase came at a time of growing concern over inflation, which remains high even as economic growth has slowed considerably, the anger over the increase also reflects broader indignation over public transportation systems in São Paulo and in other large cities, which are plagued by inefficiency, overcrowding and crime.
"Today's protests are the result of years and years of depending on chaotic and expensive transportation," said Érica de Oliveira, 22, a student who was among the demonstrators.
A large number of protesters in São Paulo on Monday were university students, but middle-aged professionals and parents with children in strollers were also present. The scene seemed at once furious and festive. Some protesters had draped Brazilian flags over their shoulders; one held up a sign that read, "Brazil Colony, until when?"
While the protest in Brasília included strong criticism of congressional leaders, many placards here in São Paulo did not direct anger at Congress, at the federal government in Brasília or even at local authorities on the state or municipal level. Still, protesters in various cities focused on symbols of government power. Here in São Paulo, they marched to the governor's palace; in Rio, to the state legislature; and in Brasília, to the Congress.
Fabio Malini, a scholar who analyzes data patterns in social media at the Federal University of Espírito Santo, said he was impressed by the movement's refusal to be defined by a single objective and by its extensive use of social media, which has enabled it to evolve fast in response to various sources of social and political tension in Brazil.
One issue surging to the fore involves anger over stadium projects in various cities ahead of the 2014 World Cup, which Brazil is preparing to host. Some projects have been hindered by cost overruns and delays, the unfinished structures standing as testament to an injection of resources into sports arenas at a time when schools and public transit systems need upgrades.
"The largest protests are happening in cities which will host World Cup games," Mr. Malini said. "Brazilians are mixing soccer and politics in a way that is new, and minority voices are making themselves heard."
Paula Ramon contributed reporting from São Paulo, and Taylor Barnes from Rio de Janeiro.
This article originally appeared in The New York Times.