The vessels will spend four months at sea, calling at nine foreign ports.
Moscow is sending an orchestra for Greece and cruise missiles for Syria in one go, according to reports.
Chinese sailors docked in Russia with a 21-gun salute as the two countries begin sea drills in the Russian region bordering North Korea.
The Baltic Fleet has called on 70 ships from its main ports and 2,000 troops ahead of a military drill on land in nearby Belarus.
The Varshavyanka class are among the quietest in the world, according to the boasts of Russian state media.
The Soversheniy—meaning Impeccable—is scheduled to join Russia's Pacific fleet next year.
Despite being taunted during its last trip to Syria, the Admiral Kuznetsov may sail for "at least" another 20 years, Russia says.
NATO members in the Baltics have grown concerned over Russia’s drills and jet flights in the northeastern European region.
Russian Baltic crews are already trained in using the new multirole fighter-bombers.
Moscow has deployed at least two cruise-missile armed frigates and intel ships.
The Admiral Essen joins its sister vessel, which arrived after the U.S. strike on Syria.
The navy has scheduled a series of tests for the cruise missile armed Krasnodar submarine.
Despite holding opposing views on NATO and the Syrian war, Russia and Turkey held joint naval exercises in the Black Sea, where military drills have already heightened tensions.
Russia's Yasen-class Kazan nuclear submarine was designed to hold long-range Kalibr cruise missiles, supersonic Oniks cruise missiles and more deadly weapons.
The Philippines' president has repeatedly shown hostility towards the U.S.
The Kremlin’s brief assessment described the work as tense and heroic.
The deployment would strongly boost Russia’s capabilities near Aleppo.
Moscow’s new base plans for deployment of land, air and sea defenses as tensions over Aleppo airstrikes grow.
The Vladimir Monomakh will be permanently deployed in Russia’s far east.
Alexander Nosatov was deputy commander of the Black Sea Fleet during the Crimea annexation.
The exercise will focus on control of the waters despite a U.N. ruling against China.
Russia has been critical of U.S. military in the Black Sea after NATO strengthened its presence in the Baltic region.
NATO and Russia are both pondering reinforcement in the Black Sea.