Russia's Defence Ministry has accused an American destroyer of coming dangerously close to a Russian frigate in the Mediterranean Sea, calling the incident a "gross violation" of international agreements.

"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 ministry added that the crew aboard the USS Gravely had committed a "gross violation of international rules on the prevention of collisions at sea" and violated a maritime agreement signed in 1972 by US and then Soviet authorities.

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."

But a US Defence Department official hit back at Moscow's claims, saying a Russian warship carried out an "unsafe and unprofessional" maritime operation near two US Navy ships on June 17.

The official, who spoke on the condition of anonymity, said the Russian Neustrashimy-class frigate came within 288 metres of the USS Gravely and within five nautical miles of the USS Harry S Truman in the eastern Mediterranean Sea.

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".

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.

AFP/Reuters