According to the statement, the direct monitoring is carried out by the Smetlivy guided missile destroyer.
The Arleigh Burke-class destroyer, armed with cruise missiles and missile interceptors, entered the southern part of the Black Sea on 8 August.
"Our naval military operations reaffirm our collective resolve to Black Sea security and enhance our strong relationships with our NATO allies and partners in the region," Vice Adm. Lisa Franchetti, the commander of U.S. 6th Fleet, said in a statement.
This is the sixth entry of a US missile destroyer into the Black Sea this year.