President Dilma Rousseff, a former leftist guerrilla who was imprisoned and tortured during the dictatorship, hailed the protests, even though her government has been a prime target of demonstrators' frustrations.
"Brazil today woke up stronger," she was quoted as saying in a statement released by her office.
"Those who took to the streets delivered a message to society as a whole and most of all to levels of government," Rousseff said. "The massive size of yesterday's protests proves the energy of our democracy, the force of the voice of the street and the civility of our population."
She didn't propose any concrete answers to soothe protesters' anger. Some cities have lowered bus fares seeking to quell outrage, so far without any apparent effect.
Sao Paulo Mayor Fernando Haddad said Tuesday that he would try to juggle the municipal budget in order to roll back the fare hikes. The group that has helped organize the protest in Sao Paulo pledged to continue until prices are lowered.
Gilberto Carvalho, Rousseff's general secretary, said the protests reflect the new demands of a richer Brazil.
"The impression is that we have overcome some obstacles, but society wants more," Carvalho said.
The office of the United Nations' High Commissioner for Human rights said it "urged the Brazilian authorities today to exercise restraint in dealing with spreading social protests in the country and called on demonstrators not to resort to violence in pursuit of their demands."
The U.N. body added in its Tuesday release that it "welcomed the statement by Brazilian President Dilma Rousseff that peaceful demonstrations are legitimate."
Human Rights Watch called on the government of Sao Paulo to make good on its promise to investigate the use of force by police against protesters. Images of police attacking protesters during a rally last Thursday helped spark the record turnouts at Monday's demonstrations, which were held in Sao Paulo, Rio, Brasilia, Belo Horizonte, Curitiba, Vitoria, Fortaleza, Recife, Belem and Salvador.