Moscow has called for the military exercises involving 5,000 NATO soldiers to be cancelled, threatening a response if necessary to protect national security.
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.
Britain rejected Russia's account of the incident.
READ MORE:UK denies Russia chased British warship
Russia annexed Crimea in 2014 and says it is Russian territory, but the peninsula is internationally recognised as part of Ukraine.
Russia's embassy in Washington called last week for the drills to be cancelled, and the Russian defence ministry said it would react if necessary to protect its own national security.
Relations between Kyiv and Moscow plummeted after Russia seized Crimea and over Russia's support for a separatist rebellion in eastern Ukraine.
Tension rose again this year when Russia massed troops on the border with Ukraine, where some of them remain along with their equipment.