The statements by the two men amount to an explicit declaration of gunboat diplomacy and an embrace of the kind of 19th-century U.S. imperialist policy in the Western Hemisphere that has been widely criticized across Latin America.

Senator Mark Warner of Virginia, the top Democrat on the Senate Intelligence Committee, said in an interview that decades-long efforts by the United States to prove it is not a colonial power in the Americas has been “all thrown out” now, and that Mr. Trump’s actions could “potentially turn the whole region against us.”

He added that the administration’s aim of dominating the Western Hemisphere — including forcibly seizing leaders in the region — could spur China and Russia to try to do the same in their perceived “spheres of influence.”