The remark was immediately seen as bolstering Mr. Maduro domestically, where he, like his predecessor, Hugo Chávez, has long warned of United States coup plots and invasions. But it has also left Latin Americans in a difficult position, forced to choose between one country accused of dictatorship and another being called an empire — or to simply condemn both.

Peru, which has taken some of the toughest stands in the region against Venezuela, issued a statement on Saturday condemning possible use of force, and Mexico said the crisis could not be resolved with soldiers. Brazil said renouncing violence was the “basis of democratic cohabitation.” And human rights groups in Venezuela rejected Mr. Trump’s threat.