Moscow has not commented on the reports from either side that its 72nd Separate Motor-rifle Brigade had abandoned its positions on the southwestern outskirts of Bakhmut.
A Russian brigade is typically formed of several thousand troops.
The 72nd Brigade pissed away three square km this morning, where I had lost around 500 men," Prigozhin said.
Early on Wednesday the unit, formed from Ukraine's nationalist Azov Battalion, reposted a video of one of Azov's founders, Andriy Biletsky, who said his forces had "defeated" the Russian brigade.
"In fact, the 6th and 7th squadrons of this brigade were almost entirely destroyed, brigade intelligence was destroyed, large number of fighting vehicles were destroyed, a considerable number of prisoners were taken," he said.