Wagner chief has been demanding more ammunition for weeks.
Prigozhin said the incident came the day after he urgently requested ammunition supplies from the commander of what Russia calls its "special military operation" (SMO).
"On March 5, I wrote a letter to the commander of the SMO grouping about the urgent need to allocate ammunition.
Since mid-January, Russia's campaign in Ukraine has been commanded personally by the chief of the general staff, Army General Valery Gerasimov.
In a video published at the weekend, he repeated earlier complaints that his men were being deprived of ammunition.
"If Wagner retreats from Bakhmut now, the whole front will collapse," Prigozhin said in the video, apparently filmed in a bunker.
In Monday's statement, he said: "We are continuing to smash the Armed Forces of Ukraine near Bakhmut.". »