Rousseff's televised address late Friday appeared to have failed to sway protesters, as activists vowed to continue the struggle and ordinarily football-mad Brazilians once again protested outside Confederations Cup games.
More than 70,000 people chanting "The Cup for whom?" rallied in the southeastern city of Belo Horizonte as Mexico edged Japan 2-1 in the football tournament seen as a dress rehearsal for next year's World Cup.
Police fired tear gas when some of the protesters hurled stones and tried to break through the security perimeter around the Mineirao stadium. Some 25 people, including five police officers, were reported injured in the clashes, and another 22 protesters were arrested.
Later, the unrest spread as shops were looted, and banks and a car dealership vandalized.
"We are against the World Cup because it masks the problems the country faces," said musician Leonardo Melo, who dismissed Rousseff's speech as "rhetoric."
Over the past two weeks, hundreds of thousands of Brazilians have protested against the billions of dollars being spent on the World Cup, accusing the government of wasting money and neglecting health, education and transport.
More than a million marched in scores of cities on Thursday.
In Sao Paulo, 35,000 people took to the streets peacefully Saturday to denounce a proposed constitutional amendment that would take away the power of independent public prosecutors to probe crimes, making it harder to combat corruption.
In the southern town of Uruguaiana, demonstrators peacefully occupied the bridge linking Brazil to Uruguay for four hours.
In the university town of Santa Maria, where a disco fire killed 242 young people in January, 30,000 people protested.
In Salvador, where Brazil beat Italy 4-2 in another Confederations Cup match, demonstrators totaled about 200 people, according to an AFP reporter.
Inside the stadium, dozens of fans brandished placards proclaiming: "Let's go to the streets to change Brazil."
West of Rio, near the Bangu prison, police confiscated Molotov cocktails, sticks and stones and arrested 30 people for looting shops and smashing furniture on the heels of a protest by around 500 people, according to the Globo G1 website.
As the Rousseff government tried to address the ever rising tide of dissatisfaction over its social policies, former football star-turned Socialist politician Romario joined the debate, praising the demonstrators and dubbing world football body FIFA "Brazil's real president."
In her address, Rousseff offered Brazilians a "great pact" between the government and the people to improve shoddy public services and stressed the need for "more effective ways to fight corruption."
But her intervention left the protesters unmoved, judging by a torrent of comments on social media websites amid the release of a new poll showing that three-quarters of Brazilians back the demonstrations.
"I was depressed listening to Dilma. It's a joke, right? Dilma treats us as if we are idiots," read one typical comment.
"We want dates and times, action. Promises are not enough," wrote another.
The protests have been largely peaceful, but some have been marred by violence and acts of vandalism, notably in Rio and Brasilia, with two deaths recorded so far.
The popular outrage, dubbed by some a "Tropical Spring" after the protest movements in the Arab world and echoing similar turmoil in Turkey this month, has come as a shock to outside observers.
The unrest even led Hollywood A-lister Brad Pitt to scrap a plan to come to Brazil to promote his new film "World War Z," the movie's distributors said Saturday.
Rousseff's predecessor and political mentor Luiz Inacio Lula da Silva left office in 2010 with a soaring 80 percent approval rating, and the social policies he initiated are credited with lifting 40 million Brazilians out of poverty.
Lula also helped raise Brazil's international profile, and the World Cup was seen as a key milestone in its emergence as a global power player after several years of steady economic growth.
But despite the nationwide obsession with football, the protesters say they feel left behind as they watch gleaming new stadiums spring up in cities paralyzed by traffic jams and clogged with aging trains and buses.