She praised them as active participants in democracy and said her government is committed to "social transformation."
Police for the most part stood back, and the atmosphere has grown festive and loud, with throngs singing and beating drums.
"It actually reminded me of Carnival in Rio," protester Fernando Jones said. "All along the avenue, people supporting the cause kept switching their lights on and off in their offices and shouting their support from the windows."
Path of rubble
But hidden in the peaceful multitudes were bands of rowdies, who kicked down doors and broke windows; looted shops, tipped over cars and set them on fire.
It left a trail of rubble down the protest routes.
Amandeep Gill woke up to the smoldering aftermath Tuesday morning.
The American, who lives and works in Rio de Janeiro, took video of smashed store fronts as he arrived at his workplace and posted it to CNN iReport.
Smoke rose out of looted shops. Across the street, a row of ATMs stood bashed, with their electronic guts hanging out.
His colleagues saw the trouble ignite the night before from their office window, they told him.
"They witnessed a car set on fire in front of our building," Gill said. "They told me they were worried that the building would catch on fire."
While asking police to back off from peaceful protesters, Dilma has condemned "isolated and minor acts of violence," telling police to confront them "with vigor."
Gill's colleagues in Rio won't let vandalism keep them off the streets.
They plan to join in Thursday's marches -- peacefully.