"On June 17, in the east of the Mediterranean Sea, the American destroyer USS Gravely came dangerously close to a Russian warship, 60 to 70 metres from the left side, and crossed the path of frigate Yaroslav Mudry at the dangerous distance of 180 metres from the bow," the ministry said in a statement.
At the time of the incident, the Russian frigate was in international waters and was not "conducting dangerous manoeuvres" in respect to the American destroyer, the statement said.
The Pentagon has reported a number of recent cases of Russian jets buzzing US planes and ships in the Baltic Sea in recent months with tensions between the two side at their highest point since the Cold War over the Ukraine crisis.
In April, the US Navy released video footage of Russian aircraft flying very close to the USS Donald Cook, including in a "simulated attack profile."
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The Pentagon "has recently accused with great perseverance Russian pilots and marines of lacking professionalism," it said.
"But this incident shows that US marines allow themselves to forget basic rules of maritime safety."
Relations between Russia and the West have nosedived over Moscow's annexation of Crimea from Kiev in March 2014 and its support for a pro-Kremlin insurgency in eastern Ukraine.