The Trump administration’s bid to replace Venezuela’s authoritarian leader Nicolás Maduro hit a roadblock after a meeting with Russian officials in Rome last year—and has never recovered.

U.S. envoy Elliott Abrams arrived at the Westin Excelsior hotel hoping to persuade Russia to withdraw its support for Mr. Maduro and to recognize Juan Guaidó as Venezuela’s legitimate leader. Russian deputy foreign minister Sergei Ryabkov instead demanded the U.S. back down from military threats and lift the economic sanctions intended to...