Brutal footage emerged this month that showed Yevgenny Nuzhin, 55, with his head taped to a brick wall.
In the unverified video, Mr Nuzhin explains that he was to be tried for defecting during the Ukraine crisis, before an unidentified man in combat clothing smashes a sledgehammer into the side of his head and neck.
The unidentified man then hits Mr Nuzhin in the head again after he collapses onto the floor.
The execution was blamed on the Wagner group, a group of mercenaries formerly of the Russian armed forces that has fought in Libya, Syria, the Central African Republic, Mali and Ukraine, among others.
Despite widespread condemnation of the video, Margarita Simonyan, the head of the RT state media outlet – a key propaganda tool for Putin – sought to defend the Wagner group.
In a filmed statement to Russians, she said: “If it wasn't for Wagner private military company, there would have been many more deaths.
“Many more mobilised men, many more crying wives and children. And you would have been the one crying.
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“You would have been among those wives, it would have been your children crying. It would have been your sons going to war and dying there.”
Her statement was criticised by Anton Gerashchenko, an adviser to the Ukrainian government, who described Simonyan as “a sweet woman in a pink shirt – praising murderers”.
He tweeted: “They have stopped being humans a long time ago.”
Simonyan previously defended the execution, saying that “Any person has the right to make a mistake, but the person has no right to lie”.
Simonyan’s comments come after Russian businessman Yevgeny Prigozhin, who founded the Wagner group in 2014, said that the execution video should be called "A dog receives a dog's death”.
He said: "Nuzhin betrayed his people, betrayed his comrades, betrayed consciously. Nuzhin was a traitor."
Prigozhin also issued a warning to other potential “traitors” in Russia, adding: ”Some traitors are holed up in offices, not thinking about their own people. Some of them use their own business jets to fly to those countries that seem neutral to us so far.
“They fly away so as not to participate in today's problems. They are traitors too.”
State-funded Russian channel RT has been banned in the UK and EU since the start of Russia’s invasion of Ukraine, while presenter Anton Krasovsky presenter was suspended for calling for the burning of Ukrainian children.
The 47-year-old apologised after saying Ukrainian children he met in the 1980s who said they saw Russia as an occupier “need to be drowned… shove them into their huts and burn them up”.