"If, because of your petty jealousy, you do not want to give the Russian people the victory of taking Bakhmut, that's your problem," Prigozhin added in the video.
A senior Ukrainian official said Russia was bringing Wagner mercenary fighters from along the front line to Bakhmut to capture it by Victory Day.
In another sign of disarray on the Russian side, former Russian deputy defence minister Colonel General Mikhail Mizintsev joined Wagner as a deputy commander, Russian pro-war social media channels reported.
Earlier, Prigozhin was pictured surrounded by corpses he said were his men, shouting abuse at Russian Defence Minister Sergei Shoigu and Chief of General Staff Valery Gerasimov.
Moscow accused Ukraine of firing drones at the Kremlin in the early hours of Wednesday in an attempt to kill Putin.