President Donald Trump said Saturday morning that Venezuela’s airspace should be considered “closed” as he weighs military action against the South American nation.

The United States has offered Venezuelan President Nicolas Maduro the chance to leave his country for Russia or elsewhere, a Republican senator said.

As part of that effort, Mr. Trump signaled on Saturday that he was ratcheting up his campaign against drug cartels, saying in a social media post that airspace above and surrounding Venezuela should b...