Russia's strategic bombers have resumed their Cold War practice of flying long-haul missions to areas patrolled by NATO and the United States, a Russian general says.

On Wednesday a Russian bomber flew over a US military base on the Pacific island of Guam and "exchanged smiles" with US pilots scrambled to track it, said Major-General Pavel Androsov, head of long-range aviation in the Russian air force.

"It has always been the tradition of our long-range aviation to fly far into the ocean, to meet (US) aircraft carriers and greet (US pilots) visually," Androsov told a news conference.