"This is a phenomenon involving the Brazilian people and the awakening of a new consciousness," the Catholic leaders said in the statement. "The protests show all of us that we cannot live in a country with so much inequality."
Rousseff had never held elected office before she became president in 2011 and remains clearly uncomfortable in the spotlight. A career technocrat and economist, she was helped into the presidency by her mentor, the tremendously popular former President Luiz Inacio Lula da Silva.
Marlise Matos, a political science professor at the Federal University of Minas Gerais, said before Rousseff spoke that officials need to take stronger action.
"The government has to respond, even if the agenda seems unclear and wide open," she said. "It should be the president herself who should come out and provide a response. But I think the government is still making strategic calculations to decide how to respond. What I'd like to see as a response is a call for a referendum on political reform. Let the people decide what kind of political and electoral system we have."
Social media and mass emails were buzzing with calls for a general strike next week. However, Brazil's two largest nationwide unions, the Central Workers Union and the Union Force, said they knew nothing about such an action, though they do support the protests.
A Thursday night march in Sao Paulo was the first with a strong union presence, as a drum corps led members wearing matching shirts down the city's main avenue. Many protesters have called for a movement with no ties to political parties or unions, which are widely considered corrupt here.
The unrest is hitting the nation as it hosts the Confederations Cup soccer tournament, with tens of thousands of foreign visitors in attendance.