"The Black Sea Fleet is monitoring the movements of the US warship in the Black Sea," a Navy official told RIA Novosti, adding that the frigate was the first U.S. warship to enter the Black Sea this year.
The vessel will call at the Bulgarian port of Varna, before visiting Ukraine's Sevastopol, and Batumi in Georgia. The Sevastopol city administration said earlier it had discussed measures to ensure the security of US seamen during their stay.
Last November, the USS Mount Whitney arrived at Sevastopol, but cut short its visit amid protests.
Locals in Ukraine's Crimea, which has a largely Russian-speaking population, frequently protest against visits by NATO ships.
Ukraine's pro-Western leadership has been pursuing NATO membership since President Viktor Yushchenko came to power in 2004. However, regular opinion polls show that the majority of Ukrainians continue to oppose NATO membership.