The death of Colonel Sergei Sukharev, of the 331st Guards Parachute Assault Regiment from Kostroma, was confirmed by state TV in Moscow.
Earlier his “liquidation” had been claimed by Ukraine’s Centre for Strategic Communication and Information Security.
“Commander of the Kostroma Airborne Regiment, Colonel Sergei Sukharev…got lost in the ‘[military] exercises’, but returned home the right way,” said the Ukrainian statement.
His deputy Major Sergei Krylov was killed alongside him, said the report.
They were among a number slain from the Kostroma regiment, seen as among Russia’s most elite fighting forces.
Russia acknowledged that senior sergeant Sergei Lebedev, sergeant Alexander Limonov and corporal Yuri Degtyaryov were also killed.
Sukharev was seen on Russian TV in January when he led his troops back from Kazakhstan where they had been sent following a wave of protests.
Russian described their mission as “peacekeeping” and Sukharev said his forces protected a vital power plant in Almaty.
Also killed in the latest Ukrainian fighting was military intelligence officer Sergey Vishnyakov, of the GRU’s 22nd Separate Special Forces Brigade.
He is believed to have been killed fighting near Mariupol in a Grad attack by Ukraine’s Azov battalion.
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Lieutenant Colonel Yuri Agarkov, from Volgograd, commander of a motorised rifle regiment, died during a special operation.
Major Ruslan Petrukhin, deputy battalion commander of the 38th Motorised Rifle Brigade, was also reported killed in action in Ukraine.
Russia has failed to announce its estimated death toll in Ukraine for more than two weeks.
There are claims it runs to around 7,000 with suspicions the true figure is being kept secret to prevent a sapping of support in Russia.
Yet the daily toll - including elite soldiers - indicates Russia is haemorrhaging its forces in a “military operation” supposedly fought to boost its security, and “denazify” Ukraine.
Moscow had deployed the 331st Guards Parachute Assault Regiment previously in Chechnya in two wars after the fall of the USSR, in Georgia in 2008, and in the Donbas in 2014.