The Project 775 warship, one of Russia's newest vessels, has a crew of 87 and took part in wars in Georgia, Syria and Ukraine, GUR said in its statement.
Sunday was the first time in a while that a night hadn’t been interrupted by air raid sirens, locals said. but sirens rang out across Ukraine on Tuesday night.
Ukraine has recently stepped up attacks on Russian targets in and around Crimea.
Footage posted on several Russian news outlets on Telegram showed powerful explosions and fires over a port area.
It was not immediately clear how Ukraine's Special Forces counted the dead and wounded in the attack.
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.
Russia's defense ministry said one serviceman was killed in the attack, while air defenses had downed a total of five missiles.
During the operation there was a clash between Ukrainian special forces on boats and a Russian fighter jet, which was damaged and forced to retreat.
Musk said he had no choice but to reject an emergency request from Ukraine "to activate Starlink all the way to Sevastopol."
The United States says it supports Ukrainian attacks on Russian military targets on the Black Sea peninsula because it should be demilitarized.
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