Dilma Rousseff
The move is viewed as an attempt by Rousseff to hold together her divided coalition government.
Polling firm Datafolha estimated 500,000 demonstrators in Sao Paulo on Sunday, the biggest rally in the city's history.
"We will win this war."
World leaders issued warnings about the rapidly spreading illness.
WHAT'S HAPPENING
"This is just a warm-up, there will be a huge mobilization in January," one protester said.
Rousseff, in office since 2011, has denied wrong-doing.
The president is accused of violating Brazil's financial laws.