Moscow has called for the military exercises involving 5,000 NATO soldiers to be cancelled, threatening a response if necessary to protect national security.
USS Ross is among 30 NATO vessels participating in the naval exercise in the Black Sea, March 3, 2017.
Ukraine and the United States have started a military exercise involving more than 30 countries in the Black Sea and southern Ukraine, despite Russian calls to cancel the drills.
Sea Breeze 2021 that began on Monday will last two weeks and involve about 5,000 military personnel from NATO and other allies, and around 30 ships and 40 aircraft. US missile destroyer USS Ross and the US Marine Corps will take part.
Ukraine says the main goal is to gain experience in joint actions during multinational peacekeeping and security operations.
Sea Breeze 2021 follows a rise in tensions between NATO and Moscow, which said last week it had fired warning shots and dropped bombs in the path of a British warship to chase it out of Black Sea waters off the coast of Crimea.