Wagner Group mercenary boss Yevgenzy Prigozhin, who is not directly related to the music producer although they have the same last name, called Iosef "impudent, aggressive and quick-tempered," and suggested that whoever recorded the call may have intended to target him instead.
In the recording, billionaire Akhmedov can be heard criticizing, among other things, the Russian government's choice to attack Ukraine when Russia still has plenty of its own "undeveloped land."
Here are some of the most striking quotes from their conversation, which gives a glimpse of real life in Russia, where truth is often obscured by propaganda.
In the call, Iosef Prigozhin says prominent Russians close to Putin blame the country's defense minister for Russia's failure to gain ground in Ukraine.
Oligarch and Putin ally Igor Sechin, Sergey Chemezov, CEO of state-owned arms company Rostec Corporation and National Guard chief Viktor Zolotov blame Defense Minister Sergei Shoigu, for "everything," Prigozhin says.
"They call him a dumb ass — behind his back, of course. And they have the f**king task of tearing him down ... They have to blame (military defeats) on someone. They act like kings, like f**king gods," he says.
"They f**ked up everything," Akhmedov says. "The question is, what comes after them?"
If we fight, then we should fight.
"This is absolutely nonsense," he says. "The president will answer for all of this. For everything. He will be held accountable ... They f**ked us up. Our children, but also their future, their f**king destiny."
Prigozhin refers to Putin and his cabinet as "criminals" and said that "even if h pushes the f**king button, there's no future for the whole nation. That's all there is to it ... For them, people are just trash.”
Putin, Akhmedov says, "Doesn't give a f**k about anything ... about the people either. He's f**king Satan ... Lilliputians, a midget with a complex."
The billionaire offers a pessimistic assessment of Russia's chances on the battlefield, and what will come next: "If we fight, then we should fight. We can't even fight. Because there's no f**king army; they can't provide it. All stolen ... Fascism will come, there will be a military dictatorship. You'll see. That's how it will all end.”