The US naval activity comes less than two weeks after Russia seized three Ukrainian ships off the coast of Crimea in the Black Sea last month in an escalation of existing tensions there.
The guided missile destroyer USS McCampbell "sailed in the vicinity of Peter the Great Bay to challenge Russia's excessive maritime claims" in a demonstrative "freedom of navigation" operation on Wednesday, the navy said.
But the Russian defence ministry claimed on Thursday that the McCampbell had not come closer than 100 kilometres (62 miles) to its territorial waters and was currently "demonstrating its bravery" 250 miles from Russian shores.
A destroyer and several warplanes nonetheless followed the US ship, which tried to "get away at maximum speed," the ministry said in a sarcastic statement carried on state television.