Prigozhin has repeatedly attacked Russian President Vladimir Putin's top military brass for what he casts as treachery.
The Wagner Group boss said his men had discovered a dozen locations in rear areas where defense ministry officials had planted various explosive devices.
Iraqi national Abbas Abuthar Witwit died on April 7, a day after arriving at a Wagner Group hospital in the Russian-controlled, eastern Ukrainian city of Luhansk, RIA FAN said.
In a sign of just how far Prigozhin may have breached the taboos of Putin's Russia, state TV ignored the fall of Bakhmut for 20 hours, and did not air his victory speech.
Kyiv is expected to soon launch a highly anticipated counteroffensive to retake Russian-occupied territory.
Prigozhin said Wagner fighters would pull out and regular Russian troops would replace them after the longest and bloodiest battle of the war.
Zelensky told the press conference that Ukrainian forces were continuing to fighting inside the city of Bakhmut and were carrying out "important tasks."
Russia said on Saturday it had completely taken the city, which, if confirmed, would mark an end to the longest and bloodiest battle of the 15-month war.
Russia claimed on Saturday to have fully captured the smashed eastern Ukrainian city.
Ukraine's spokesperson for military east command denies Russia's Wagner has taken full control of Bakhmut.