Ms. Rousseff's closer engagement of Cuba—she is visiting the island before a trip to the White House— is the latest example of Brazil's strategy to expand its regional influence by offering subsidized loans to poorer nations.

"I would imagine that the U.S. would privately hope that Brazil will play a mediating role in issues that concern us, like human rights," said Cynthia Arnson, the director of the Latin American program at Washington's Woodrow Wilson International Center for Scholars.

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