Washington has released a video showing a Russian fighter jet making a close pass over a US Navy vessel in the Black Sea, off Crimea, in an incident underscoring tensions reminiscent of the Cold War between the two superpowers.

The clip was distributed to counter Moscow's claim that it scrambled several aircrafts to head away a guided missile destroyer that was allegedly acting aggressively near the Russian border.

The 40-second footage shows a Russian SU 24 jet flying low past the USS Ross, coming quite close to the warship.

The US Navy said the encounter happened in international waters and the SU 24 carried no weapons.

"Ross continued on her mission after observing the aircraft return to base," a message accompanying the video read. "At no time did Ross act aggressively, nor did she deviate from her planned operations."

Earlier Russian media quoted a source in Crimea's security forces as saying that the vessel was moving along the edge of Russia's territorial waters, heading in their direction on Sunday (31 May).

"The crew of the ship acted provocatively and aggressively, which concerned the operators of monitoring stations and ships of the Black Sea Fleet," the source said.

Close encounters between Russian warplanes and Western forces have significantly augmented in the Black Sea as well as in the Baltic area since hostilities in eastern Ukraine began last year.

Crimea, a Ukrainian peninsula, was annexed by Russia in March 2014 in a move that was not recognised by most of the international community.