RIO DE JANEIRO — Brazil’s president, Dilma Rousseff, said Tuesday that she was postponing a state visit to the United States, delivering a sharp rebuke to the Obama administration over revelations that the National Security Agency had spied on her, her inner circle of top aides and Brazil’s largest company, the oil giant Petrobras.

The move by Ms. Rousseff showed how the disclosures of United States surveillance practices by Edward J. Snowden, the former N.S.A. contractor, were aggravating Washington’s ties with an array of nations, including European allies like Germany.

In the case of Brazil, Latin America’s largest nation, the move to effectively suspend a state visit to the United States — a remarkably rare decision in the annals of diplomacy — threatens to unravel years of Washington’s efforts to recognize Brazil’s rising profile in the developing world and blunt the growing influence of China, which has surpassed the United States as Brazil’s top trading partner.

President Obama spoke with Ms. Rousseff by telephone for 20 minutes on Monday night, but failed to persuade her to go through with the visit, which had been scheduled for late October. A series of news reports about N.S.A. spying in Brazil had clearly irked Ms. Rousseff in recent weeks, and her government demanded a full explanation from Washington.