According to Sputnik news agency, earlier in the day, Moscow urged the United States and its NATO allies to stop military operations in the Black Sea region, calling instead for "multilateral efforts" aimed at maintaining stability, and for states in the region to resolve problems without unwanted "help" from outside powers.
Along with the naval maneuvers, a Russian Su-24M attack aircraft carried out a mock bombing run against the British warship, according to the ministry.
According to the military, the British warship was warned that deadly force would be used if it violated Russia's borders. The ship was said to have ignored the warning.
The Royal Navy has yet to comment on the incident.
According to Sputnik, the HMS Defender's automatic identification system (AIS) signal shows the ship to be situated about 40 km off Crimea as of 14:15 local time, and to be sailing southeast.
But, according to the BBC, Britain has denied Russian reports that its military fired warning shots at a UK destroyer in the Black Sea.
The British Ministry of Defence (MoD) said "no warning shots have been fired at HMS Defender".
It added that the ship was sailing in Ukrainian waters.
The MoD said the Russians were carrying out a gunnery exercise in the Black Sea and provided prior warning of their activity.
KI/PR