The senior commanders were killed during heavy fighting on Sunday in eastern Ukraine, where Russian forces have been stepping up assaults on the key city Sievierodonetsk, in the Donbas region.
Russian state television said that Major-General Roman Kutuzov was killed in eastern Ukraine, reports the Reuters news agency.
City's respite from fighting shattered during one morning
The report did not provide more details and the Russian army did comment.
Unconfirmed reports on social media also said another top Russian officer, Lieutenant-General Roman Berdnikov, commander of the 29th Army, died on Saturday.
Russia officially lists military deaths as state secrets even in times of peace and has not updated its official casualty figures in Ukraine since March 25, when it said that 1351 Russian soldiers had been killed since the start of the Ukraine invasion on February 24.
The UK Ministry of Defence said that Russia appeared to have suffered significant losses amongst mid-level and junior-ranking officers in Ukraine.
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Last month it was reported US intelligence was helping the Ukraine military kill Russian generals in the war.
Citing unnamed senior officials, the New York Times claimed US intelligence have detected the whereabouts of several battlefield headquarters where Russian generals were based.
That information was then shared with Ukrainian units, who used artillery and other targeted strikes to kill the senior Russian officers.
The US also provided vital information on the location of Russia's Black Sea flagship the Moskva, which was struck and sunk by Ukraine in April.