The military exercise is the first naval maneuver that takes place in the Black Sea between both countries.
That is the first time the Bridge of Friendship joint naval exercise is taking place in the Black Sea as it used to be held in the Mediterranean.
Visits to the Black Sea by U.S. warships have nothing to do with U.S. security and are motivated by domestic politics, said Russian senator Alexei Pushkov.
Russia dismissed a statement by the leaders of France and Germany accusing it of using military force and carrying out illegitimate checks on Ukrainian vessels.
Russia's FSB security service said early on Monday its border patrol boats had seized three Ukrainian naval vessels in the Black Sea near Crimea.
The Ukrainian navy accused Russia on Sunday of opening fire on some of its ships in the Black Sea, striking one vessel and wounding a crewmember.
Ancient Greek trading ship dating back more than 2,400 years has been found virtually intact at the bottom of the Black Sea, the world's oldest known shipwreck.
Russia accused Britain's Royal Air Force of intercepting its military aircraft over the Black Sea in a dangerous fashion designed to provoke Moscow after the RAF made two such interceptions in a single week.
Russian naval forces in the Black Sea region have been put on heightened alert to discourage Ukraine from trying to disrupt the soccer World Cup.
Delegates on Monday arrived in Russia for talks aimed at ending the Syrian conflict.
Turkish authorities say they stopped 313 migrants on the Black Sea attempting to reach Balkan countries in the last two days.