BUENOS AIRES — President Obama has been lambasted for spying in Brazil, accused of being a warmonger by Bolivia, dismissed as a “lost opportunity” by Argentina, and taunted in Nicaragua by calls for Latin America to draw up its own list of state sponsors of terrorism — with the United States in the No. 1 spot.

But now Latin American leaders have a new kind of vocabulary to describe him: They are calling him “brave,” “extraordinary” and “intelligent.”

After years of watching his influence in Latin America slip away, Mr. Obama suddenly turned the tables this week by declaring a sweeping détente with Cuba, opening the way for a major repositioning of the United States in the region.

Washington’s isolation of Cuba has long been a defining fixture of Latin American politics, something that has united governments across the region, regardless of their ideologies. Even some of Washington’s close allies in the Americas have rallied to Cuba’s side.