"We can do many things a lot better in Brazil," said Rousseff yesterday, the day after the protesters demanded cheaper transport and more investment in education and health care as well as a tougher fight against endemic corruption.
"People have a right to criticise," Rousseff said, adding that she would staunchly defend that right.
Appealing for unity Rousseff, who promised to meet with the leaders of peaceful demonstrations as well as workers and community leaders, said: "I am the president of all Brazil -- of those who support the demonstration and those who do not."
But she added she would not stand by if demonstrations turned violent, as they have in several cities that have seen looting and attacks on public buildings including the foreign ministry in the capital Brasilia.
"The government cannot stand by as people attack public property ... And bring chaos to our streets," she stressed.
Nevertheless, Brazil needs the protesters' "energy and creativity", Rousseff said.
"We need to inject oxygen into our political system, and make it more transparent and resistant" to the tough challenges facing a country marked by extreme disparity between rich and poor."
Earlier Rousseff's chief of staff Gilberto Carvalho warned that the country must plan for the possibility that the unrest could continue during World Youth Day, the Catholic youth festival due to be held in Rio in late July, which Pope Francis is due to attend.
Many Brazilians are angry over the multi-billion-dollar expense of preparations for the World Cup and for the 2016 Summer Olympics, saying the money would be better spent on making education, health services and public transportation better and cheaper.
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