so-called 'shell shortages'. There are five times more of them than there should have been," he said in an audio message to his press service.
He called on Russians to demand publicly, but without resorting to demonstrations, that the defence ministry give ammunition to his troops.
The raw power struggle at the heart of Russia's war in Ukraine has prompted commentators to speculate whether Prigozhin is being squeezed out by Gen Gerasimov, who was recently put in charge of the campaign.
Pro-Kremlin pundit Sergei Markov said Russians who backed the war were clearly backing Prigozhin and the squabble would undermine the defence ministry's authority.
Russia expert Mark Galeotti said that if ammunition was being withheld then, along with the rotation of Wagner troops away from Bakhmut, "it sets [the] scene for regulars to deliver Putin his first victory (however meaningless) for some time".
"We will not leave Bakhmut," vowed Prigozhin in his audio message. "We'll simply die in double the numbers until all [the Wagnerites] are finished. And when the Wagnerites are completely finished, most likely Shoigu and Gerasimov will have to pick up machine guns."