"We are not flying with nuclear weapons during our patrols. They are not aboard. There are only training weapons," the head of strategic aviation, General Pavel Androsov, was quoted as saying.
He said the main aim of the flights was to improve training for pilots, which in recent years "was virtually stopped".
President Vladimir Putin announced the resumption of long-range flights in international air space while he attended military exercises on August 17.
Such flights were standard during the Cold War standoff with the United States and its western European allies, but were abandoned in 1992 amid financial difficulties that followed the Soviet collapse.
The airplanes involved in the patrols are the Tu-160, Tu-95MS, Il-78, and MiG-35, Androsov said.
Russian bombers had been making increasingly frequent flights near US territory in the lead-up to Putin's announcement, while Britain and Norway have recently scrambled jets to intercept Russian planes near their airspace.
Androsov played down fears of renewed tension, saying "our contacts in the air are friendly".