By Brian Winter and Jeferson Ribeiro
SAO PAULO/BRASILIA (Reuters) - Brazilian President Dilma Rousseff promised on Friday to hold a dialogue with members of a protest movement sweeping the country, but also said she would do whatever is necessary to maintain order in the wake of widespread vandalism and looting.
"We cannot live with this violence that shames Brazil," she said in a nationally televised address. "All institutions and public security forces should prevent, within the limits of the law, every form of violence and vandalism."
Rousseff spoke even as new demonstrations broke out on Friday, including one that for several hours blocked most passengers from entering or leaving the country's busiest international airport, outside Sao Paulo.
The protests have come out of seemingly nowhere over the past week. More than 1 million people took to the streets on Thursday in the biggest demonstrations in Brazil in 20 years.
The nameless, leaderless movement - composed largely of students and the middle class - has pulled together a wide range of grievances including bad public transport and healthcare, corruption, and the billions of dollars that the government is spending to host next year's World Cup.
Rousseff, a former guerrilla who herself protested a military rule during the 1960s, praised the peaceful majority of protesters and said she would listen to their demands.
Speaking calmly but firmly, she said Brazil has a "historic opportunity" to harness the energy from the protests and make improvements. But she warned the movement could be ruined by violence like that seen on Thursday, when protesters smashed buildings, looted stores and set fires in a dozen cities.
Rousseff said it was her "obligation to listen to the voice of the streets, as well as dialogue with all segments" of society peacefully protesting.
The president, who is not known for initiating talks, did not specify what such a process would look like.
After her speech, the hashtag #calabocadilma - "Shut up, Dilma" in Portuguese began trending on Twitter accompanied by withering comments attacking her government.
Friday's protests were much smaller than those on Thursday. There were signs of a backlash against the movement on Friday, and one prominent leftist group said it would stop organizing marches for now because of discord and violence.
Unlike other recent protest movements such as the Arab Spring, Brazil's demonstrators are not targeting individual politician and Rousseff remains relatively popular.
Many are part of the middle class, which benefited from a recent economic boom. But they are upset about paying European-level taxes for what some describe as African-level public services.
Rousseff made a specific appeal for calm during a warm-up event underway for the World Cup. Clashes between protesters and police have occurred outside stadiums, terrifying many fans and tourists.
A recent economic slowdown and rising inflation has crimped the government's budget, meaning it probably cannot offer a major public investment plan without making painful spending cuts elsewhere - unlikely with an election looming next year.
Rousseff in her speech cited plans such as setting aside future oil royalties for education and importing doctors from abroad. She has previously made these proposals and they have faced resistance in Congress and elsewhere.
Mayors of several cities tried to yield to one of the protesters' main demands this week by rolling back a recent hike in bus and subway fares, but the demonstrations only grew.
The festive atmosphere that had attracted many students and even their parents to demonstrations over the past week took a big and possibly lasting hit on Thursday night.
TV images showed masked youths looting stores, setting fires and defacing buildings including the foreign ministry in Brasilia, which had its windows smashed. The violence was widespread, occurring in at least a dozen cities, and appeared to be fueled by fringe movements and common criminals taking advantage of the disorder.
Two people died as a result of the protests, local media reported, including one death caused by a car plowing into a crowd. More than 60 were injured in Rio de Janeiro alone.
Radio, TV, Twitter and other social media crackled on Friday with condemnations of the violence, while the unity that had prevailed among protesters at the heart of the movement also showed signs of breaking down.
The Free Fare Movement in Sao Paulo, an activist group that was instrumental in the rise of the protests, said it would stop organizing new demonstrations for now after street fights broke out among protesters with different objectives on Thursday.
Douglas Belome, a bank teller and member of the Free Fare group, said things turned ugly when some protesters sought to prevent left-wing political parties from waving their flags.
"At least for now, there are no new demonstrations scheduled," he told Reuters, expressing regret for the violence.
World soccer body FIFA on Friday condemned the recent violence but said it had not considered cancelling either the warmup tournament, known as the Confederations Cup, or the big event next year.
Italy coach Cesare Prandelli told reporters that his team was banned from leaving the hotel because of the unrest.
Polls have shown that a large majority of Brazilians support the protesters and their aims. But the demonstrators' primary tactic of blocking main roads has begun to wear on some people.
"I support these (protests), but I think it's out of control," said Nilson Chabat, a 31-year-old gas station attendant on his way to work on Friday in Sao Paulo. "Many of us are angry but you can't just go make a mess every day."
(Additional reporting by Silvio Cascione and Caroline Stauffer; Editing by Todd Benson and Xavier Briand)