The captain of the Moskva warship was killed during an explosion and subsequent fire on board, according to Ukrainian reports.
First Rank Captain Anton Kuprin, 44, was killed after the warship was hit by two Ukrainian Neptune anti-ship missiles, according to Kyiv sources.
He “died during an explosion and fire on board the former flagship of the Black Sea Fleet of the Russian Federation,” said Anton Gerashenko, advisor to the Kyiv interior ministry.
The official added: “We do not mourn.”
Other sources support the claim that Capt Kuprin was killed.
Russia has claimed the crew was evacuated but there are increasing reports of lives lost on the battleship.
A “farewell ceremony” to the cruiser is due to be held in Sevastopol on Friday at a monument in honour the 300th anniversary of the Russian fleet .
There was no immediate confirmation from Moscow on Kuprin, but Russia has failed to announce many prominent military deaths in the 51-day war.
It comes as Captain Alexey Bogomolov, of the 25th separate regiment of GRU special forces (Stavropol), was said to have been killed in action in the conflict.
The funeral for GRU agent Bogomolov will reportedly be held in the Tambov region on Saturday.