The US Navy said the USS Mount Whitney had entered the region to conduct routine naval operations with US allies and NATO partners.
The Black Sea, particularly the area near Crimea, which Russia annexed from Ukraine in 2014, is an area of particular security sensitivity for Moscow.
The TASS news agency quoted the Russian Defense Ministry as saying: “The forces and contingents of the Black Sea Fleet have begun monitoring the movements of the flagship (Mount Whitney).”
Russian President Vladimir Putin said on Monday that Russian forces would be able to monitor Mount Whitney “through binoculars or (by having it) within range of their defense systems.”
Russia, which severed ties with NATO last month, has repeatedly complained about the alliance’s activity near its borders or what it sees as its post-Soviet sphere of influence.
But the US show of military might was warmly welcomed by Ukraine.
Ukrainian Foreign Minister Dmytro Kuleba said on Twitter: “Hello Mount Whitney. Ukraine has demanded and strongly supports a massive presence of our US and NATO allies in the region.”