Washington yesterday criticised the manoeuvre -- which was dramatically caught on camera -- with US military command slamming it as "unsafe and unprofessional."
Su-24 planes were conducting test flights in the area and "having observed the ship, turned away in observance of all safety measures," the defence ministry spokesman Igor Konashenkov said in a statement posted on the ministry's Facebook page.
"Frankly speaking, we don't understand such a sore reaction from our US colleagues," the statement added.
The US military's European command said one flyby -- one of several -- consisted of a "simulated attack profile" and came within 30 feet (nine metres) of the ship USS Donald Cook.
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"These actions have the potential to unnecessarily escalate tensions between countries and could result in a miscalculation," it said.
A senior US defence official, speaking on condition of anonymity, said: "This is more aggressive than anything we've seen in some time."
Ties between Russia and the West have plunged to their lowest point since the Cold War over Moscow's annexation of the Crimean peninsula from Ukraine in 2014 and its support for separatist rebels in the east of the country.