The arrival of the U.S. warship in the region has sparked anger in Moscow following the Kremlin's complaints about NATO activities near its borders.
On Tuesday (November 2), Russia's Black Sea naval forces rehearsed destroying enemy targets and activated air defense systems at the presence of two U.S. warships in the area, the Interfax news agency reported.
USS Mount Whitney will join the U.S. destroyer USS Porter which entered the Black Sea last week for a routine patrol.
Russia has repeatedly accused NATO of carrying out provocative activities close to its borders.
The alliance says it is determined to reinforce the security of member states close to Russia following Moscow's annexation of Crimea and its backing for pro-Russian rebels in eastern Ukraine.