The Russian Defence Ministry did not immediately respond when asked by Reuters to confirm or deny that Sokolov had been killed in the attack on Crimea, which Russia seized and annexed in 2014.
The Ukrainian military said Friday's attack had targeted a meeting of the Russian navy's leadership in the city of Sevastopol.
"After the strike on the headquarters of the Russian Black Sea Fleet, 34 officers died, including the commander of the Russian Black Sea Fleet. Another 105 occupiers were wounded. The headquarters building cannot be restored," the special forces said on the Telegram messaging app.
It was not immediately clear how Ukraine's Special Forces counted the dead and wounded in the attack.
The new death and casualty figures are a steep increase from what Ukraine's intelligence chief, Kyrylo Budanov, told Voice of America on Saturday when he said at least nine people were killed and 16 others wounded in the attack that left the building smoldering.
He also said Alexander Romanchuk, a Russian general commanding forces along the key southeastern front line, was "in a very serious condition".
Each side has at times exaggerated enemy losses since Russia's full-scale invasion of Ukraine 19 months ago and each says little about its own losses.
Russian-installed officials confirmed the Ukrainian attack on Friday, saying that at least one missile struck the fleet headquarters.
Ukraine has stepped up attacks in the Black Sea and Crimea as Ukrainian forces press on with a nearly four-month-old counteroffensive to take back Russian-occupied territory.
Russian authorities on Monday reported new explosions on Crimea.
According to Russian-appointed governor Mikhail Razvoshev, Monday's blasts were the result of a "controlled detonation" at the heavily damaged headquarters in the city of Sevastopol.
Further blasts were also planned for the evening, Razvoshev wrote on Telegram.
The information could not be independently verified.
United Nations-backed human rights experts said on Saturday they found new evidence of war crimes committed by Russian forces as Ukrainian President Volodymyr Zelenskiy welcomed the arrival of the first Abrams tanks sent by the United States.
The UN Independent Commission of Inquiry on Ukraine said it found evidence of crimes committed by both sides in the war but far more by Russian forces, including instances of torture, some of it fatal, and rape of women as old as 83.
It said it was also looking into allegations that Russian forces committed genocide.
Zelenskiy thanked allies on Telegram for their support in announcing the anticipated arrival of the tanks.
He did not say how many tanks had arrived but the US has said it was sending 31 tanks.
with DPA and AP
