Ukraine’s military also confirmed the killing of Gen Kutuzov, without offering further details.
Russian state media have confirmed the death of one of Moscow’s top generals during heavy fighting in Ukraine’s eastern Donbas region.
Maj Gen Roman Kutuzov was killed leading an assault on a Ukrainian settlement in the region, a reporter with the state-owned Rossiya 1 said.
Alexander Sladkov said Gen Kutuzov had been commanding troops from the self-declared 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.”
Ukraine’s military also confirmed the killing of Gen Kutuzov, without offering further details about the circumstances.
His death comes as rumors circulated on social media that a second senior officer, Lt Gen Roman Berdnikov, commander of the 29th Army, was also killed in fighting over the weekend. The BBC cannot independently verify the claims.
Russian commanders have been increasingly forced to the front in an attempt to drive forward the invasion and Moscow has confirmed the deaths of four senior generals.
Kyiv claims to have killed 12 generals and Western intelligence officials say at least seven senior commanders have been killed.
But there has been confusion over reports of the deaths of several other Russian officers. Three generals that Ukrainian forces claimed to have killed have subsequently been reported to be alive.
In March, Ukrainian forces said Maj Gen Vitaly Gerasimov had been killed outside the country’s second city of Kharkiv. However, on 23 May Russian state media said he had been awarded a state honour and dismissed reports of his death.
Another commander, Maj Gen Magomed Tushaev, also appeared to be still alive and periodically appears in videos posted to social media.
And on 18 March, Kyiv alleged that Lt Gen Andrey Mordvichev had been killed in an airstrike in the Kherson region. However, he later appeared in a video meeting with Chechen leader Ramzan Kadyrov and on 30 May BBC Russia confirmed that he was still alive.
The deaths of generals are rarely officially acknowledged in Russia. In the case of Maj Gen Vladimir Frolov, no information about his death had appeared in state media prior to his funeral in St Petersburg in April.
Russia lists military deaths as state secrets even in times of peace and has not updated its official casualty figures in Ukraine since 25 March, when it said that 1,351 Russian soldiers had been killed since President Vladimir Putin launched his invasion of Ukraine on 24 February.
In March, an official within President Volodymyr Zelensky’s inner circle told the Wall Street journal 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. They added that the officers were then targeted either with sniper fire or artillery.
Last month, the New York Times reported that the US has provided intelligence to Ukraine, allowing them to target a number of the generals who have been killed in action.
Lt Gen Yakov Rezantsev was reportedly killed by a Ukrainian strike on the Chornobaivka airbase near the city of Kherson.
He was promoted to lieutenant general last year, and was commander of the 49th combined army of Russia’s southern military district.
He is said to have taken part in Russia’s military operation in Syria.
Maj Gen Oleg Mityaev reportedly died somewhere near the city of Mariupol, a city in south-east Ukraine which was the scene of a protracted Russian siege.
The nationalist Azov regiment claimed to have killed him.
He was a commander of the Russian army’s 150th motorised rifle division, a relatively new unit formed in 2016, and based in the Rostov region close to the Ukrainian border.
Ukraine claims that the unit was created in order to take part in the conflict in separatist-controlled areas of eastern Ukraine, although Russia denies that its military was involved in fighting there.
Maj Gen Andrei Kolesnikov, of the 29th combined army, was killed in fighting on 11 March, according to official Ukrainian sources.
The circumstances of his death were not given.
After Kolesnikov became the third Russian general reportedly killed in Ukraine, one western official told the Press Association that the Russian army may be suffering from low morale, which is why high-ranking military officers are moving closer to the front line.
Maj Gen Andrey Sukhovetsky, a deputy commander at the same unit as Gerasimov, was reportedly killed by a sniper on 3 March.
Like Gerasimov, Sukhovetsky was part of Russia’s military operations in Crimea and in Syria.
Unlike the other generals, Sukhovetsky’s death was reported in the Russian media and Russian President Vladimir Putin confirmed in a speech that a general had died in Ukraine.