Ukraine earlier ordered 19 Federal Security Service (FSB) officers to leave Sevastopol, where the fleet is based, before December 28.
"The special service command has already left Sevastopol," the source said. "Black Sea Fleet counterintelligence officers will be moved from Sevastopol to Novorossiisk."
He said the Russian counterintelligence officers had been based in the Crimea with the permission of Ukraine, which had sought cooperation in fighting terrorism and extremism.
However, after the August 2008 war in Georgia, Valentyn Nalivaichenko, the head of the Ukrainian Security Service, said the FSB presence was unnecessary.
Ukrainian President Viktor Yushchenko pledged last Monday to force Russia's Black Sea Fleet to leave the Crimea before 2017.
Russia's Black Sea Fleet uses a range of naval facilities in the Crimea, including the Sevastopol base, as part of a 10-year lease agreement signed in 1997.
Yushchenko has led calls for Russia to pack up and pull out of Ukraine when the lease expires in 2017, although Russia hopes to extend it.
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