SAO PAULO – Thousands of anti-government demonstrators again took to streets in several Brazilian cities Saturday after the president broke a long silence to promise reforms, but the protests were smaller than those of recent days and with only scattered reports of violence.

Police estimated about 20,000 demonstrators gathered in a central square in the city of Belo Horizonte, largely to denounce legislation that would limit the power of federal prosecutors to investigate crimes in a country where many are fed up with the high rate of robberies and killings. Many fear the law also would hinder attempts to jail corrupt politicians and other powerful figures.

Dilma Rousseff, a former leftist guerrilla who was tortured under Brazil’s long military dictatorship, made a televised 10-minute appearance on Friday backing the right to peaceful protest but sharply condemning violence, vandalism and looting.

She also promised to be tougher on corruption and said she would meet with peaceful protesters, governors and the mayors of big cities to create a national plan to improve urban transportation and use oil royalties for investments in education.

Much of the anger behind the protests has been aimed at costly bus fares, high taxes and poor public services such as schools and health care.

Many Brazilians, shocked by a week of protests and violence, hoped that Rousseff’s words would soothe tensions and help avoid more violence, but not all were convinced by her promises of action.

Still, a rapidly growing crowd blocked Sao Paulo’s main business street, the Avenida Paulista, to press their demands.

Victoria Villela, a 21-year-old university student, said she was “frustrated and exhausted by the endless corruption of our government.

“It was good Dilma spoke,” she said, “but this movement has moved too far … I think the protests are going to continue for a long time and the crowds will still be huge.”