The defence ministry said in a statement it dispatched Su-27 jets to check out the US P-8 Poseidon planes as they "twice tried to get close to the Russian border over the Black Sea without their transponders turned on".
"After the Russian fighters got close to the spy planes for visual confirmation and to determine their wing numbers the American aircraft changed course sharply and flew away," the statement said.
A US defence official said a Russian plane flew within 10 feet (3 metres) of a US spy plane in a move "considered unsafe and unprofessional".
The Russian statement said that this was "not the first attempt" by NATO aircraft to get close to the country's borders to spy on major military drills currently taking place on the Ukraine border and the annexed Crimea peninsula.
Relations between Russia and the West are currently at their lowest point since the Cold War over Moscow's seizure of Crimea from Ukraine and alleged fuelling of a separatist conflict in the ex-Soviet country.
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