President Nicolás Maduro of Venezuela had become a pariah among fellow Latin American leaders as his beleaguered country staggered toward dictatorship. But a threat by President Trump to use the American military against Mr. Maduro’s government has united those leaders in a different direction: demanding that the United States keep out of the region’s affairs.

“The possibility of a military intervention shouldn’t even be considered,” Juan Manuel Santos, Colombia’s president, said on Sunday during a visit by Vice President Mike Pence to the region. “America is a continent of peace. It is the land of peace.”

Mr. Santos’s response to Mr. Trump’s remarks — echoed by many other Latin American leaders in recent days — could endanger a fragile alliance against what many fear is the first dictatorship to emerge in the region in decades, analysts say.

“Threatening military action undermines the strongest Latin American consensus in support of democracy that I have seen since the end of the Pinochet regime,” said Mark L. Schneider, an adviser at the Americas program of the Center for Strategic and International Studies, referring to the Chilean military dictatorship led by Augusto Pinochet.