High commanders were killed on Sunday during heavy fighting in eastern Ukraine, where Russian forces have stepped up assaults on the key city of Sievierodonetsk in the Donbas region.
Russian state television reported that Major General Roman Kutuzov was assassinated in eastern Ukraine, Reuters reports.
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The report did not provide further details and the Russian military did comment.
Unconfirmed reports on social media also said that another senior Russian official, Lieutenant General Roman Berdnikov, commander of the 29th Army, was killed on Saturday.
Russia officially classifies military deaths as state secrets even in peacetime and has not updated its official casualty figures in Ukraine since March 25, when it said 1351 Russian soldiers had been killed since beginning of the invasion of Ukraine on February 24.
The United Kingdom Ministry of Defense said that Russia appeared to have suffered significant losses among middle and lower level officials in Ukraine.
A Ukrainian tank in the Donetsk region of eastern Ukraine. Strong fighting for control of a key city continues. (AP)
It was reported last month that US intelligence was helping the Ukrainian army kill Russian generals in the war.
Citing unnamed senior officials, the New York Times claimed that US intelligence had detected the whereabouts of several battlefield headquarters where Russian generals were based.
This information was then shared with Ukrainian units, which used artillery and other targeted attacks to kill senior Russian officers.