Russian state media reported earlier this month that the USS Porter, a U.S. naval destroyer, had entered the Black Sea on a routine deployment, a move it said raised hackles in Moscow because it had recently been fitted with a new missile system.
Under the Montreux Convention, countries which don't have a Black Sea coastline cannot keep their warships there for more than 21 days. NATO members Turkey, Romania and Bulgaria are all Black Sea Basin countries.
Russia, which annexed Ukraine's Crimea in 2014, has its own Black Sea Fleet based at Sevastopol.
"If a decision is made to create a permanent force, of course, it would be destabilising, because this is not a NATO sea," Russian news agencies quoted Andrei Kelin, a senior Foreign Ministry official, as saying.
"It (the Black Sea) has nothing to do with the alliance. I do not think this would improve our relations with NATO."
Kelin spoke ahead of a NATO summit in Warsaw next month which is being held at a time when relations between Russia and the alliance are severely strained over Moscow's role in the Ukraine crisis.
NATO is considering what more it can do to deter what it sees as growing Russian aggression. Moscow says it poses no threat to the alliance.
NATO Secretary-General Jens Stoltenberg on Wednesday criticised new Russian snap checks on combat readiness, saying they undermined stability. Russia's Defence Ministry retorted angrily, accusing NATO of fanning anti-Russian hysteria before its summit.
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