A Russian fighter jet has made close-range passes for more than 90 minutes near an American warship in the Black Sea amid diplomatic tensions between the US and Russia over Ukraine.

Pentagon said on Monday that the Russian Fencer made 12 passes and flew within 900 metres of the destroyer USS Donald Cook on Saturday at about 150 metres above sea level.

"This provocative and unprofessional Russian action is inconsistent with international protocols and previous agreements on the professional interaction between out militaries," Army Colonel Steve Warren, a Pentagon spokesman, said.

The fighter appeared to be unarmed and never was in danger of coming in contact with the ship, said the officials, but it did not respond to radio queries and warnings used by the US warship. The passes ended without incident.

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