Brazil's political crisis deepened on Sunday when opposition parties seized the occasion of nationwide anti-corruption demonstrations to push for a change in power. An estimated 1.8 million people took to the streets in peaceful protests across the country, demanding the resignation of President Dilma Rousseff.

Similar demonstrations have been held every few months for more than a year, as a massive graft scandal known as Lava Jato unfolds. Until now, the opposition has largely remained a silent partner – but with pressure intensifying on Ms. Rousseff and her Workers' Party, as the investigation draws closer to her inner circle, her political opponents appear set to try to capitalize.

Ms. Rousseff and her political mentor, former president Luiz Inacio Lula da Silva, are increasingly threatened by Lava Jato, which saw construction and supply firms trade an alleged $2-billion (U.S.) in bribes for contracts at the state-run oil firm Petrobras, with a chunk of the cash funnelled to political parties. Mr. da Silva was briefly detained by police and questioned on March 4, and last week faced a new set of state criminal charges relating to the same money-laundering case.

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Protesters carried banners demanding the President leave office, and that Mr. da Silva be jailed. Inflatable puppets of the ex-president in prison stripes were a popular accessory, and as always at right-leaning protests, the national football jersey or other clothing embossed with the flag was the outfit of choice.

On Friday, Ms. Rousseff gave an impromptu press conference in which she reiterated that she had been democratically elected and would not resign. But she is the subject of impeachment proceedings and the past 10 days have been difficult for her. While Ms. Rousseff has always maintained that she knew nothing of the graft scheme that played out at Petrobras, and she has not been personally implicated in it, she was chair of the company, as Minister of Energy at the time, and her insulation from Lava Jato is eroding rapidly.

A senator charged in the scandal who cut a plea deal has, according to media reports, implicated her in an attempt to block the investigation. And both federal and state prosecutors are now investigating Mr. da Silva's role. Many protesters on Sunday expressed their support – even adoration – for Sergio Moro, a federal court judge in the state of Curitiba who has overseen the Lava Jato prosecutions. But Mr. Moro has drawn criticism from some in government because of the growing perception that Lava Jato is focusing on the left-leaning Workers' Party and its allies, even though politicians from almost all parties have been named as participants.

Judge Moro issued a statement about the protests on Sunday in which he said, "it is important that the elected authorities and the parties listen to the voice of the streets and commit equally to fighting corruption."

Aecio Neves, leader of the Brazilian Social Democracy Party (PSDB), who narrowly lost the last presidential election to Ms. Rousseff, attended demonstrations in both Sao Paulo city and Belo Horizonte, in his home state of Minas Gerais. But the attempt to seize the political moment was not well-received in all quarters; he and his entourage were forced to leave the Sao Paulo protest after half an hour because many demonstrators were hostile, arguing the PSDB did not belong at an event protesting corruption in politics, according to Brazilian media reports.

Mr. Neves has been mentioned four times by people attempting to cut plea deals in Lava Jato; two allegations were deemed to have insufficient evidence to proceed. Two are not yet under investigation but have not been ruled out.

Maria do Socorro Braga, a professor of political science at the Federal University of Sao Carlos in Sao Paulo, said the demonstrations will not be sufficient to force Ms. Rousseff out. "The plea bargains [by Lava Jato defendants who turn state's witness] are going to be more important in this process than the protests," she said. "Everything about these – if new proof comes to light, for example – will have an impact on her support in Congress."

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Sunday's protests, much like similar events in the past, were dominated by middle-class Brazilians – in Rio, a city where more than two-thirds of citizens are black and mixed-race, the vast majority of protesters were white.

"The President is very arrogant: she won't listen to society," said Pericles Mattos, 48, a business administrator who marched with his family. "And Lula influences her. She won this election with illegal money from Petrobras so it was an unfair election."

Marcelo Nader, 49, who owns a Panama hat company, also brought three generations of his family. "We're here to demand the government leave, because they're stealing everything we have, everything the country has, they're destroying the country," he said. "She destroyed Petrobras when she was in charge there – she says she didn't know anything about [the graft] – it's ridiculous."

Like many protesters, he expressed disbelief and frustration that Ms. Rousseff's supporters could have won the past election. "We're a very young democracy and people don't know how to vote properly," he said. "There are some people who know – but the majority don't."

Mr. Nader said that Ms. Rousseff must resign, and be succeeded by Vice-President Michel Temer, who is under investigation by the electoral court for using illegal resources to finance his campaign. "Nobody likes him," Mr. Nader said. "But you prefer somebody who beats you to someone who kills you."

But Prof. Braga said the demonstrators' demands fly in the face of the constitution and democratic process. "Dilma was elected, she won at the ballot boxes against the biggest opposition party," she said. "To take a President out, respecting the constitution, you need proof."

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Ms. Rousseff's support, however, appears to be eroding. Her main coalition ally, the Brazilian Democracy Movement Party (PMDB), says it will decide within 30 days whether to remain in government.

"I want Dilma to leave because I'm not seeing anything get better – I voted for her but I'm very disappointed," said Lilia Ciszesande, 32, who was sweeping the street during the protest. "Things went better for poor people in her first term. I think we should have new elections."

Demonstrations in support of Ms. Rousseff and her party are scheduled for March 20. On Sunday night, she said the "peaceful character" of the protests demonstrated the "maturity" of Brazilian democracy and showed a country that "knows how to live with divergent opinions."

With a report from Manuela Andreoni