Russia has long expressed concern that its neighbors could become NATO members and that such developments could spark war.
The S-400 system is considered the most advanced in the world.
The men were captured during a violent confrontation with Russian navy ships on Sunday.
U.S. air presence over the Black Sea angered Moscow.
The bridge restricts Ukrainian access to the Black Sea.
The country's armed forces have rallied 8,000 troops for the drills across 19 training ranges, including two breakaway regions in neighboring Georgia.
Europe's southeastern sea was once dominated by the Soviet Union but now has three NATO allies and two NATO aspiring members on it.
The Black Sea is fascinating to archaeologists because its zero-oxygen "dead zone" preserves shipwrecks and artifacts for thousands of years.
Russia said U.S. pilots should avoid traveling near Crimea—or expect Moscow's jets to fly close by.
The U.S. surveillance plane was flying in international airspace.
Moscow has repeatedly protested U.S. military presence in a region where it once enjoyed sweeping naval dominance.
The Pentagon says Russia caused violent turbulence, but Moscow's former air force deputy commander says the U.S. should not have been in the Black Sea.
Since seizing Crimea from Ukraine, Russia has reinforced military assets in Black Sea waters around it and is now building its first land link to the territory.
The Varshavyanka class are among the quietest in the world, according to the boasts of Russian state media.
NATO allies have deployed a limited number of aircraft in Romania, which borders Ukraine, to assist with its air patrols. Russia is not happy.
The Black Sea is a priority area of reinforcement for the Russian navy following the annexation of nearby Crimea in 2014.
The British and Turkish ships dock in Odessa as Kiev warns about a regression into deadly combat.
The P-8A Poseidon was in the area on a routine operation, the U.S. Navy said.
Russia fired missiles only miles away from NATO forces in the volatile Black Sea region, where the U.S. has accused Moscow of threatening its interests.
Ukraine's fleet is looking for minesweepers and coast guard ships for the Black Sea.
Secretary General Jens Stoltenberg said NATO was reacting to Russian reinforcements in the region but did not want a new Cold War.
Abkhazia and South Ossetia consider themselves independent from Tbilisi.
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