MOSCOW — Russian bombers have flown to the island of Guam — home to a major American military base — for the first time since the Cold War in an exercise intended to show the Kremlin’s resurgent military power, an air force general said yesterday.

Two Tu–95 bombers reached Guam, an American territory, this week, and their crews smiled at the pilots of the American fighter jets that scrambled to intercept them, Major General Pavel Androsov said.

“Whenever we saw U.S. planes during our flights over the ocean, we greeted them,” General Androsov said. “On Wednesday, we renewed the tradition when our young pilots flew by Guam in two planes. We exchanged smiles with ourcounterparts who flew up from a U.S. carrier and returned home.” The flight to the Pacific island was part of a three-day exercise that saw Russian strategic bombers making 40 sorties and launching eight cruise missiles, said General Androsov, who commands Russia’s long-range bomber force. The incident coincided with a week-long exercise by the American military off Guam involving more than 22,000 troops, dozens of ships, and hundreds of aircraft. American officials have said the war games, which began Tuesday, were not connected in any way to world events or targeted at any country.

During the Cold War, Soviet bombers routinely flew far over the Arctic, Atlantic, and Pacific oceans — the areas from where they would launch nuclear-tipped cruise missiles at America in case of war. The maneuvers came to a halt after the post-Soviet economic meltdown, but booming oil prices have allowed Russia to pour money into military budgets.

The Kremlin also has taken an increasingly assertive posture on the international stage amid increasingly chilly relations with the American government and NATO. In recent years, the military has sent strategic bombers to areas off Norway and Iceland, as well as the regions across the Bering Strait from Alaska.