The operation, dubbed Citadel, was conducted at night and resulted in the capture of "important enemy equipment" and the platform being blown up.
The number of ships has increased to 13 units, including five large amphibious ships and one surface missile carrier.
The region was hit by powerful storms on Sunday and the governor's office said the bad weather prevented air and sea vessels from carrying out searches.
Russia has previously reported a number of incidents in which its fighter jets were scrambled to intercept military planes from Norway, another NATO member, over the Barents Sea.
Russia's Naval Aviation has been particularly diligent in its maritime air patrol operations recently, according to the British Defense Ministry.
After it invaded Ukraine last year, Moscow closed off the Black Sea ports of one of the world's biggest suppliers of grain.
Ukraine's special forces said on Monday they had killed Sokolov, Moscow's top admiral in Crimea, along with 33 other officers in a missile attack last week.
It was not immediately clear how Ukraine's Special Forces counted the dead and wounded in the attack.
Lavrov accused the West of a neo-colonial mindset in its overtures to the Global South to win backing for Ukraine in the war.
Friday's attack on the Russian Black Sea Fleet headquarters in Crimea is also rumoured to have killed Admiral Viktor Sokolov, commander of Russia’s Black Sea Fleet.
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