A reporter for state-owned Rossiya 1 said Major General Roman Kutuzov was killed in an attack on a Ukrainian settlement in the region.
Alexander Sladkov said that General Kutuzov commanded troops from the self-proclaimed Donetsk People’s Republic.
Russia’s Defense Ministry has not commented on the reports.
“The general had led soldiers into attack as if there are not enough colonels,” Mr Sladkov wrote on the Telegram social media app. “On the other hand, Roman was the same commander as everyone else, albeit a higher rank.”
The Ukrainian military also confirmed the killing of General Kutuzov without giving further details of the circumstances.
His death came after rumours spread on social media that a second senior officer, 29th Army Commander Lieutenant General Roman Berdnikov, had also been killed in fighting over the weekend. The BBC could not independently verify the claims.
Russian commanders are forced to the front in an attempt to advance the offensive, and Moscow has confirmed the deaths of three senior generals.
Kyiv claims to have killed 12 generals, and Western intelligence officials say at least seven senior commanders have been killed.
But the news of the deaths of several other Russian officials has led to confusion. Three generals claimed to have been killed by the Ukrainian military were later reported to be alive.
In March, the Ukrainian military said Major General Vitaly Gerasimov had been killed outside Kharkiv, the country’s second city. However, on May 23, Russian state media said that he had been awarded state honours and dismissed reports of his death.
Another commander, Major General Magomed Tushayev, also appears to be alive and appears from time to time in videos posted on social media.
The death of generals in Russia is rarely officially acknowledged. In the case of Major General Vladimir Frolov, no information about his death was revealed to the state media before his funeral in St Petersburg in April.
Russia had listed 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 the February 24 invasion of Ukraine by President Vladimir Putin. Since its launch, 1,351 Russian soldiers have been killed.
In March, an official in President Volodymyr Zelensky’s inner circle told Wall Street magazine that a team of Ukrainian military intelligence officers had been tasked with locating and targeting Russia’s officer class.
“They look for high profile generals, pilots, artillery commanders,” the official said. He said the officers were then either targeted by sniper fire or artillery.
