SÃO PAULO—Hundreds of thousands of Brazilians made a noisy and impassioned call on Sunday for the removal of President Dilma Rousseff, whose leftist government is plagued by a sprawling corruption scandal and an economic meltdown that has humbled Latin America’s largest country.

Protesters poured into the streets in scores of cities waving banners and chanting slogans in what organizers and police estimated was among the largest antigovernment turnouts since Ms. Rousseff ascended to power in 2011.

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