"Despite recent reports, @USNavy #USSRoss as of 30 minutes ago and for the foreseeable future is in port #Odesa, #Ukraine to support #ExerciseSeaBreeze", the official Twitter account of the exercise led by the US Sixth Fleet said.
Earlier in the day, media outlets reported, citing vessel tracking websites, that the US destroyer was sailing toward the peninsula.
Last week, the UK destroyer HMS Defender made inroads into Russia's territorial waters near Cape Fiolent in Crimea, prompting the Russian Navy to fire warning shots to divert the vessel. London denied the shots were fired at all, even though Russia's security service, the FSB, released video footage of the encounter, confirming Moscow's account of events.
A BBC correspondent who was aboard the British ship at the time of the incident also said he saw over 20 aircraft overhead and two Russian coast guard boats that shadowed Defender.