The leader added she would soon hold a meeting with leaders of the protest movement, governors and the mayors of major cities. But it remained unclear exactly who could represent the massive and decentralized groups of demonstrators taking to the streets, venting anger against woeful public services despite a high tax burden.
Rousseff said that her government would create a national plan for public transportation in cities — a hike in bus and subway fares in many cities was the original complaint of the protests. She also reiterated her backing for a plan before congress to invest all oil revenue royalties in education and a promise she made earlier to bring in foreign doctors to areas that lack physicians.
"I want institutions that are more transparent, more resistant to wrongdoing," Rousseff said in reference to perceptions of deep corruption in Brazilian politics, which is emerging as a focal point of the protests. "It's citizenship and not economic power that must be heard first."
The leader, a former Marxist rebel who fought against Brazil's 1964-1985 military regime and was imprisoned for three years and tortured by the junta, pointedly referred to earlier sacrifices made to free the nation from dictatorship.
"My generation fought a lot so that the voice of the streets could be heard," Rousseff said. "Many were persecuted, tortured and many died for this. The voice of the street must be heard and respected and it can't be confused with the noise and truculence of some troublemakers."
Edvaldo Chaves, a 61-year-old doorman in Rio's upscale Flamengo neighborhood, said he found the speech convincing.
"I thought she seemed calm and cool. Plus, because she was a guerrilla and was in exile, she talks about the issue of protests convincingly," Chaves said. "I think things are going to calm down. We'll probably keep seeing people in the streets but probably small numbers now."
But Bruna Romao, an 18-year-old store clerk in Sao Paulo, said Rousseff's words probably wouldn't have an impact.
"Brazilians are passionate," she said. "We boil over quickly but also cool down fast. But this time it's different, people are in full revolt. I don't see things calming down anytime soon."
Trying to decipher the president's reaction to the unrest had become a national guessing game, especially after some 1 million anti-government demonstrators took to the streets nationwide Thursday night to denounce everything from poor public services to the billions of dollars spent preparing for next year's World Cup soccer tournament and the 2016 Olympics in Brazil.
The protests continued Friday, as about 1,000 people marched in western Rio de Janeiro city, with some looting stores and invading an enormous $250 million arts center that remains empty after several years of construction. Police tried to disperse the crowd with tear gas as they were pelted with rocks. Police said some in the crowd were armed and firing at officers.
Local radio was also reporting that protesters were heading to the apartment of Rio state Gov. Sergio Cabral in the posh Rio neighborhood of Ipanema.
Other protests broke out in the country's biggest city, Sao Paulo, where traffic was paralyzed but no violence reported, and in Fortaleza in the country's northeast. Demonstrators were calling for more mobilizations in 10 cities on Saturday.
The National Conference of Brazilian Bishops came out in favor of the protests, saying that it maintains "solidarity and support for the demonstrations, as long as they remain peaceful."
"This is a phenomenon involving the Brazilian people and the awakening of a new consciousness," church leaders said in the statement. "The protests show all of us that we cannot live in a country with so much inequality."
Rousseff had never held elected office before she became president in 2011 and remains clearly uncomfortable in the spotlight.
She's the political protege of former President Luiz Inacio Lula da Silva, a charismatic ex-union leader whose tremendous popularity helped usher his former chief of staff to the country's top office. A career technocrat and trained economist, Rousseff's tough managerial style under Silva earned her the moniker "the Iron Lady," a name she has said she detests.
While Rousseff stayed away from the public eye for most of the week, Roberto Jaguaribe, the nation's ambassador to Britain, told news channel CNN Friday the government was first trying to contain the protests.
He labeled as "very delicate" the myriad demands emanating from protesters in the streets.
"One of our ministers who's dealing with these issues of civil society said that it would be presumptuous on our part to think we know what's taking place," Jaguaribe said. "This is a very dynamic process. We're trying to figure out what's going on because who do we speak to, who are the leaders of the process?"
Marlise Matos, a political science professor at the Federal University of Minas Gerais, said before Rousseff spoke that answer wasn't good enough.
"The government has to respond, even if the agenda seems unclear and wide open," she said. "It should be the president herself who should come out and provide a response. But I think the government is still making strategic calculations to decide how to respond. What I'd like to see as a response is a call for a referendum on political reform. Let the people decide what kind of political and electoral system we have."
Social media and mass emails were buzzing with calls for a general strike next week. However, Brazil's two largest nationwide unions, the Central Workers Union and the Union Force, said they knew nothing about such an action, though they do support the protests.
A Thursday night march in Sao Paulo was the first with a strong union presence, as a drum corps led members wearing matching shirts down the city's main avenue. Many protesters have called for a movement with no ties to political parties or unions, which are widely considered corrupt here.
Several cities have cancelled the transit fare hikes that had originally sparked the demonstrations a week ago, but the outrage has only grown more intense.
Demonstrations for Saturday have been called by a group opposing a federal bill that would limit the power of prosecutors to investigate crimes.
Most protesters have been peaceful, and crowds have taken to chanting "No violence! No violence!" when small groups have prepared to burn and smash. The more violent demonstrators have usually taken over once night has fallen.
The unrest is hitting the nation as it hosts the Confederations Cup soccer tournament, with tens of thousands of foreign visitors in attendance.
Carlos Cardozo, a 62-year-old financial consultant who joined Friday's protest in Rio, said he thought the unrest could cost Rousseff next year's elections. Even as recently as last week, Rousseff had enjoyed a 74 percent approval rating in a poll by the business group the National Transport Confederation.
"Her paying lip service by saying she's in favor of the protests is not helping her cause," Cardozo said. "People want to see real action, real decisions, and it's not this government that's capable of delivering."