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."
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 a $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.
Other protests broke out in in the country's biggest city, Sao Paulo, where traffic was paralyzed but no violence was reported, and in Fortaleza in the country's northeast. Demonstrators were calling for more mobilizations in 10 cities on Saturday.
With Pope Francis scheduled to visit Brazil next month, the National Conference of Brazilian Bishops issued a statement expressing "solidarity and support for the demonstrations, as long as they remain peaceful."