The Russian Defense Ministry, quoted by Interfax, said the maneuvers in the Black Sea were pre-planned.
Russia announced last month its Navy would stage a series of military exercises involving its entire fleet from January to February, from the Pacific to the Atlantic.
Three of the Russian warships had passed through the Turkish strait into the Black Sea on Tuesday, according to a Reuters witness.
Turkish sources said another three warships were expected to appear on Wednesday.
The ships included the Korolev, Minsk and Kaliningrad, which set sail on the Bosphorus on Tuesday. Meanwhile the ships Pyotr Morgunov, Georgy Pobedonosets, and Olenegorsky Gornyak are scheduled to pass on Wednesday.
Russia has amassed more than 100,000 troops near the Ukrainian border.
Moscow denies having plans to attack Ukraine, but seeks comprehensive security guarantees, including promises of no missile deployment near its borders, reduction of NATO's military infrastructure and a ban on Ukraine from joining the alliance.
By law, Turkey as a NATO member can close its straits for transit if Russia takes military action against Ukraine.
"Turkey is authorized to close the strait to all foreign warships in times of war or when aggression is threatened," said Yoruk Isik, geopolitical analyst and head of the Istanbul-based consultancy Bosphorus Observer.
"Also, it is authorized to deny transit of merchant ships belonging to countries that are at war with Turkey," he added.
Turkey, which shares maritime borders with Ukraine and Russia on the Black Sea, said any military conflict was unacceptable and told Moscow that any invasion was unwise.
But President Tayyip Erdogan has also offered to mediate in the dispute between Moscow and Kiev.
Ankara has good relations with both countries, although Erdogan has said he will do what is necessary as a member of NATO in the event of a Russian invasion.
French President Emmanuel Macron, said on Tuesday after talks in the Kremlin with Russian President Vladimir Putin that he believed steps could be taken to de-escalate the crisis and called on all parties to remain calm.
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