Russia's foreign ministry has vowed to respond to the entry of a US Navy ship into the Black Sea with unspecified "measures".
The USS Porter entered the Black Sea a few days ago "as part of a regularly scheduled deployment", the US Navy said.
The guided-missile destroyer arrived at the port of Varna in Bulgaria, a NATO member, on 8 June, the US Navy's Sixth Fleet said in a statement.
"The ship's operations in the Black Sea are meant to enhance maritime security and stability, readiness and naval capability with our allies and partners," it said.
Russian media said it was expected to continue on to Ukraine and Georgia, both countries that have been in territorial dispute with pro-Russian groups.
Andrei Kelin, a senior foreign ministry official, was reported as saying by Russian state news agency RIA: "Of course, this does not meet with our approval and will undoubtedly lead to response measures."
US officials said the US military would also have two aircraft carriers in the Mediterranean this month.
The deployments are taking place ahead of a NATO summit in Warsaw in July.
USS Porter's deployment to the Black Sea has raised hackles in Moscow because the ship has recently been fitted with a new missile system.
The US Navy says it is maintaining its operation in the sea - which provides the Russian navy's only direct access to the Mediterranean - in accordance with international law and the various agreements that govern the passage of military ships.
But Mr Kelin said the deployment of US aircraft carriers in the Mediterranean was a show of force which in his view deepened a chill in ties between Moscow and Washington.
Diplomatic relations have been at a low as a result of Russia's actions in Ukraine and Syria, where Russian forces are assisting the regime of Bashar al Assad.
"As regards the overall situation of course there is a definite increase and stoking of tensions in our relations," Mr Kelin was reported as saying.
"It is all being done on the eve of the Warsaw NATO summit. It is a show of force."
USS Porter is normally based at Rota, Spain, while the US Sixth Fleet is headquartered at Naples.
On Tuesday, Russian online newspaper Pravda.ru quoted an unnamed Russian official as saying that any US ship that attacked his country "would only have five to 10 minutes to live".
